HeliusMCT-UsersGuide-Abaqus

User’s Guide Helius:MCT™ Version 4.0 for ABAQUS February 1, 2011 Abstract This document describes the use of Helius:MCT for Abaqus/Standard in performing enhanced finite element analysis of composite structures. For questions, comments or further information, contact Firehole Composites at [email protected]. Legal Notices Copyright 2011, Firehole Technologies, Inc. Helius:MCT is a trademark of Firehole Technologies, Inc. Any use of the Helius:MCT trademark requires the prior written consent of Firehole Technologies, Inc. Abaqus/Standard is a trademark of Dassault Systemes S.A. and Dassault Systemes SIMULIA Corp.

Helius:MCT User’s Guide – Abaqus Page 2 of 113

Table of Contents 1 INTRODUCTION TO HELIUS:MCT ................................................................................................... 5

1.1 A NOTE ON THE HELIUS:MCT- LINEAR VERSION ............................................................................ 5 1.2 HELIUS:MCT INTERACTION WITH ABAQUS/STANDARD .................................................................... 6 1.3 HELIUS:MCT SUPPORT DOCUMENTATION ..................................................................................... 8

2 GENERAL REQUIREMENTS FOR ABAQUS INPUT FILES .......................................................... 10

2.1 IDENTIFICATION AND DEFINITION OF HELIUS:MCT MATERIALS ....................................................... 10 2.2 DEFINITION OF EXTRANEOUS STIFFNESS PARAMETERS FOR CERTAIN TYPES OF ELEMENTS ............ 11 2.3 NONLINEAR SOLUTION CONTROL PARAMETERS FOR HELIUS:MCT ................................................ 11 2.4 REQUESTING OUTPUT OF SOLUTION VARIABLES THAT ARE UNIQUE TO HELIUS:MCT ...................... 12

3 USING ABAQUS/CAE TO CREATE ABAQUS INPUT FILES FOR USE WITH HELIUS:MCT ...... 13

3.1 CREATING COMPOSITE MATERIALS WITH THE HELIUS:MCT PLY GUI ............................................. 13 3.2 CREATING COHESIVE MATERIALS WITH THE HELIUS:MCT COHESIVE GUI...................................... 22 3.3 SPECIFYING EXTRANEOUS STIFFNESS PARAMETERS REQUIRED BY CERTAIN ELEMENT TYPES ........ 25 3.4 STEP MODIFICATIONS ................................................................................................................. 26 3.5 REQUESTING MCT STATE VARIABLE OUTPUT FOR COMPOSITE MATERIALS ................................... 28 3.6 REQUESTING MCT STATE VARIABLE OUTPUT FOR COHESIVE MATERIALS ..................................... 30 3.7 DELETING A HELIUS:MCT MATERIAL ........................................................................................... 30

4 USING A TEXT EDITOR TO CONVERT PRE-EXISTING ABAQUS INPUT FILES FOR USE WITH HELIUS:MCT .................................................................................................................................. 31

4.1 DEFINING A HELIUS:MCT COMPOSITE MATERIAL ......................................................................... 31 4.2 DEFINING A HELIUS:MCT COHESIVE MATERIAL ............................................................................ 38 4.3 MODIFYING THE SECTION DEFINITIONS ........................................................................................ 39 4.4 MODELING ISSUES FOR IMPOSING TEMPERATURE CHANGES ......................................................... 41 4.5 NONLINEAR SOLUTION CONTROL PARAMETERS FOR HELIUS:MCT ................................................ 41 4.6 REQUESTING OUTPUT OF THE MCT STATE VARIABLES ................................................................. 42 4.7 MODELING DAMAGE TOLERANCE IN COMPOSITE MATERIALS ......................................................... 43

5 RUNNING HELIUS:MCT ON LINUX................................................................................................ 45

6 EXAMINING HELIUS:MCT RESULTS WITH ABAQUS/VIEWER ................................................... 46

6.1 USING CONTOUR PLOTS TO VIEW THE MCT STATE VARIABLES ....................................................... 46 6.2 DETECTION OF GLOBAL STRUCTURAL FAILURE .............................................................................. 51

APPENDIX A USER MATERIAL CONSTANTS FOR COMPOSITE MATERIALS .......................... 55

APPENDIX A.1 USER MATERIAL CONSTANT #1: SYSTEMS OF UNITS ................................................... 56 APPENDIX A.2 USER MATERIAL CONSTANT #2: PRINCIPAL MATERIAL COORDINATE SYSTEM ............... 58 APPENDIX A.3 USER MATERIAL CONSTANT #3: PROGRESSIVE FAILURE ANALYSIS .............................. 61 APPENDIX A.4 USER MATERIAL CONSTANT #4: PRE-FAILURE NONLINEARITY ..................................... 63 APPENDIX A.5 USER MATERIAL CONSTANT #5: POST-FAILURE NONLINEARITY AND ENERGY-BASED

DEGRADATION........................................................................................................... 64 APPENDIX A.6 USER MATERIAL CONSTANT #6: HYDROSTATIC STRENGTHENING................................. 70 APPENDIX A.7 USER MATERIAL CONSTANT #7: THERMAL RESIDUAL STRESSES ................................. 71 APPENDIX A.10 USER MATERIAL CONSTANT #10: NOT CURRENTLY USED ........................................... 73 APPENDIX A.11 USER MATERIAL CONSTANT #11: AVERAGE ELEMENT THICKNESS ............................... 73 APPENDIX A.12 USER MATERIAL CONSTANT #12: MATRIX POST-FAILURE STIFFNESS / MATRIX

DEGRADATION ENERGY ............................................................................................... 1 APPENDIX A.13 USER MATERIAL CONSTANT #13: FIBER POST-FAILURE STIFFNESS / FIBER DEGRADATION

ENERGY ..................................................................................................................... 3

APPENDIX B USER MATERIAL CONSTANTS FOR COHESIVE MATERIALS ............................... 5


APPENDIX B.1 USER MATERIAL CONSTANT #1: DAMAGE CRITERIA ...................................................... 5 APPENDIX B.2 USER MATERIAL CONSTANTS #2-4: MATERIAL STIFFNESS ............................................. 6 APPENDIX B.3 USER MATERIAL CONSTANTS #5-7: DAMAGE INITIATION ................................................ 6 APPENDIX B.4 USER MATERIAL CONSTANTS #8-11: DAMAGE EVOLUTION ............................................ 7

APPENDIX C EXTRANEOUS STIFFNESS PARAMETERS ............................................................ 10

APPENDIX C.1 DESCRIPTION OF THE EXTRANEOUS STIFFNESS PARAMETERS ...................................... 11 APPENDIX C.2 FORMATTING OF THE EXTRANEOUS STIFFNESS PARAMETERS....................................... 13 APPENDIX C.3 CALCULATION OF EXTRANEOUS STIFFNESS PARAMETERS ............................................ 16 APPENDIX C.4 USING ABAQUS/CAE TO INSERT THE EXTRANEOUS STIFFNESS PARAMETERS................ 24

APPENDIX D MCT STATE VARIABLES FOR COMPOSITE MATERIALS .................................... 27

APPENDIX E MCT STATE VARIABLES FOR COHESIVE MATERIALS ....................................... 36

APPENDIX F TROUBLESHOOTING ............................................................................................... 37

APPENDIX F.1 MANUAL RESOLUTION OF KEYWORD CONFLICTS PRODUCED BY ABAQUS/CAE .............. 37 APPENDIX F.2 SYSTEM ERROR CODES ............................................................................................. 39

Table of Figures FIGURE 1: SCHEMATIC DIAGRAM OF THE INDIVIDUAL COMPONENTS OF THE HELIUS:MCT SOFTWARE

AND THEIR INTERACTION WITH THE ABAQUS/STANDARD SOFTWARE COMPONENTS ...................... 7 FIGURE 2: THE HELIUS:MCT PLY GRAPHICAL USER INTERFACE (GUI) .............................................. 14 FIGURE 3: KEYWORDS EDITOR SHOWING THE KEYWORD STATEMENTS THAT COLLECTIVELY DEFINE A

HELIUS:MCT MATERIAL................................................................................................................... 22 FIGURE 4: HELIUS:MCT COHESIVE GUI IN ABAQUS/CAE..................................................................... 23 FIGURE 5: LOCATION OF INCREMENTATION PARAMETERS IN THE EDIT STEP DIALOG BOX .................. 27 FIGURE 6: GENERAL SOLUTION CONTROLS EDITOR DIALOG BOX ........................................................ 28 FIGURE 7: LOCATIONS OF SDV AND SECTION POINT OUTPUT PARAMETERS IN THE EDIT FIELD

OUTPUT REQUEST DIALOG BOX ...................................................................................................... 29 FIGURE 8: KEYWORDS CONFLICT DIALOG BOX ...................................................................................... 30 FIGURE 9: LOCATION OF SECTION POINTS WITHIN AN ELEMENT CONTAINING 4 MATERIAL PLIES ........ 43 FIGURE 10: CONTOUR PLOT OPTIONS DIALOG BOX ............................................................................... 47 FIGURE 11: COMPARISON OF A BANDED CONTOUR PLOT AND A QUILT CONTOUR PLOT USING THREE

DISCRETE COLOR CONTOURS TO REPRESENT DISTRIBUTION OF SDV1=1,2,3 ............................ 48 FIGURE 12: SECTION POINTS DIALOG BOX ............................................................................................ 49 FIGURE 13: ENVELOPE, QUILTED CONTOUR PLOTS OF SDV1 AT SEVERAL DIFFERENT POINTS IN TIME

DURING A PROGRESSIVE FAILURE ANALYSIS .................................................................................. 50 FIGURE 14: 8-PLY COMPOSITE PLATE UNDER IMPOSED AXIAL DISPLACEMENT .................................... 52 FIGURE 15: THE GLOBAL STRUCTURAL FORCE IS OBTAINED BY SUMMING THE VERTICAL REACTIONS

FORCES AT ALL NODES ALONG THE TOP EDGE OF THE COMPOSITE PLATE ................................... 52 FIGURE 16: GLOBAL STRUCTURAL FORCE VS. GLOBAL STRUCTURAL DEFORMATION .......................... 53 FIGURE A17. THE FIBER DIRECTION FOR EACH ELEMENT IS INDICATED BY THE RED LINES ................. 59 FIGURE A18: HELIUS:MCT SOLUTION FOR FAILURE PROPAGATION IN THE 0° PLIES OF A COMPOSITE

LAMINATE LOADED IN TENSION ........................................................................................................ 62 FIGURE A19: COMPARISON OF PREDICTED VS. MEASURED LONGITUDINAL SHEAR RESPONSE FOR A

TYPICAL FIBER-REINFORCED COMPOSITE LAMINA. ......................................................................... 63


FIGURE A20: HELIUS:MCT STRESS-STRAIN SOLUTIONS FOR THE CENTRAL 90° PLY WITHIN A (0/90/0) LAMINATE UNDER AXIAL TENSION, SHOWING THE EFFECT OF INCLUDING THE POST-FAILURE NONLINEARITY FEATURE .................................................................................................................. 65

FIGURE A21: STRESS/STRAIN RESPONSE FOR A LINEAR DEGRADATION USING ENERGY-BASED DEGRADATION. ................................................................................................................................. 66

FIGURE A22 ENERGY-BASED LINEAR DEGRADATION INTERVAL PARTITIONING. ................................... 68 FIGURE A23 LINEAR DEGRADATION FOR LARGE ENERGY PROBLEM USING SECANT MODULUS

INTERVAL DIVISIONS. ....................................................................................................................... 69 FIGURE B24. TYPICAL COHESIVE MATERIAL TRACTION-DISPLACEMENT CURVE. ................................... 8 FIGURE B25. COHESIVE MATERIAL RESPONSE........................................................................................ 9 FIGURE C26: HELIUS:MCT GUI WITH IM7_8552 SELECTED AS A MATERIAL ...................................... 18 FIGURE C27: ABAQUS COMMAND WINDOW FROM WHICH TO RUN THE DATACHECK ANALYSIS ........... 19 FIGURE C28: SEQUENCE OF COMMANDS TO RUN A DATACHECK ANALYSIS ......................................... 20 FIGURE C29: LOCATIONS OF SECTION POISSON’S RATIO, THICKNESS MODULUS, AND TRANSVERSE

SHEAR STIFFNESS SETTINGS IN THE EDIT COMPOSITE LAYUP DIALOG BOX ................................ 24 FIGURE C30: LOCATIONS OF HOURGLASS STIFFNESS SETTINGS IN THE ELEMENT TYPE DIALOG BOX 25 FIGURE C31: LOCATION OF HOURGLASS STIFFNESS PARAMETERS IN THE KEYWORDS EDITOR ......... 26 FIGURE F32. THE PROCESS OF ACCESSING THE KEYWORD EDITOR IN ABAQUS/CAE ...................... 38 FIGURE F33: KEYWORDS EDITOR, SHOWING A KEYWORD CONFLICT CAUSED BY AN EXTRANEOUS

*DEPVAR STATEMENT ................................................................................................................... 39


Functionality not available in Helius:MCT Linear

1 Introduction to Helius:MCT

Helius:MCT is composed of a set of software modules and a composite material library that integrate seamlessly with the Abaqus/Standard finite element analysis system, providing the user with state-of-the-art material modeling capability for unidirectional and woven fiber-reinforced composite materials. Helius:MCT utilizes a form of multiscale material modeling that is based on Multicontinuum Theory (MCT) which has been under continuous joint development by the University of Wyoming and Firehole Composites over the past 15 years. The MCT modeling methodology provides an unsurpassed combination of accuracy, efficiency and convergence robustness in predicting damage evolution and material failure in composite materials. In sharp contrast to traditional continuum mechanics, where physical quantities of interest (e.g., stress and strain) are averaged over the entire heterogeneous microstructure of the composite material, MCT retains the identities of the distinct material constituents within the microstructure. Consequently, physical quantities of interest (e.g., stress and strain) are averaged over each individual constituent material. These constituent average quantities provide much deeper insight into the thermo-mechanical behavior of the composite material than the traditional composite average quantities. To briefly summarize, MCT focuses on two concepts: 1) the development of relationships between the various constituent average quantities of interest, and 2) the development of relationships that link the composite average quantities to the constituent average quantities. For a complete discussion of MCT and the advantages that it provides in the analysis of composite materials, refer to the Helius:MCT Theory Manual. Additionally, Helius:MCT can provide delamination predictions using Abaqus cohesive elements (COH2D4 and COH3D8) defined with a Helius:MCT Cohesive user material. The delamination model uses some of the same material models provided by Abaqus/Standard, however, Helius:MCT provides robust convergence. Helius:MCT allows analyses to use both ply level and cohesive level progressive failure models without a significant increase in analysis time.

1.1 A Note on the Helius:MCT- Linear Version Firehole Composites also offers a limited-functionality version of Helius:MCT referred to as

Helius:MCT-Linear. Helius:MCT-Linear provides users access to advanced multi-scale analysis, constituent level stress and strain values and multi-scale failure indices when running linear elastic finite element simulations.

Helius:MCT-Linear does not provide access to many of the advanced, nonlinear functionalities that are available in the full version of Helius:MCT such as progressive failure modeling, material non-linearity, cohesive functionality and other advanced features.

In an effort to delineate in this document the features that are not available in the Linear version of Helius:MCT, the following graphic will be displayed when describing a feature that requires a license to the full-featured version of Helius:MCT.


1.2 Helius:MCT Interaction with Abaqus/Standard In an Abaqus structural-level finite element analysis of a composite structure, Helius:MCT quickly and accurately decomposes the composite average stress/strain field into constituent average stress/strain fields. The constituent average stress states are then used by Helius:MCT to predict damage evolution and material failure individually for each constituent material that is present in the microstructure. Subsequently, Helius:MCT homogenizes the current damaged microstructure in order to provide an accurate assessment of the current composite average stiffness for use in the structural-level finite element analysis. Helius:MCT is designed to provide this enhanced composite modeling capability without significantly increasing the time required to run the structural-level finite element analysis. For example, using Helius:MCT to enhance a structural-level finite element analysis usually increases the time required to perform a single structural-level equilibrium iteration by only two to three percent (a very small price to pay for the increased solution accuracy provided by Helius:MCT). However, Helius:MCT is specifically developed to increase the convergence robustness of structural-level progressive failure simulations; consequently, analyses that are enhanced by Helius:MCT are more likely to successfully resolve the entire load history while using fewer total equilibrium iterations. Figure 1 shows a schematic diagram of the individual components of the Helius:MCT software and their interaction with the Abaqus/Standard software components. In Figure 1, bold rectangles indicate the components of the Abaqus/Standard finite element modeling package, while ovals indicate the individual components of the Helius:MCT software. In Figure 1, the Helius:MCT Graphical User Interface (GUI) is accessed from within Abaqus/CAE and assists the user in defining the Abaqus input file parameters that are required during a finite element analysis that employs Helius:MCT. The Helius:MCT User-Defined Material Subroutine (see Figure 1) calculates constitutive relations and computes stresses for the Abaqus/Standard finite element code. The Helius:MCT User-Defined Material Subroutine contains all of the MCT constitutive relations for the individual constituents (fiber and matrix) and the homogenized composite material. In addition, the Helius:MCT User-Defined Material Subroutine contains the constituent-based failure criteria and the nonlinear constituent damage algorithms which degrade the stiffness of the constituents and the homogenized composite material to reflect the current damage state of the composite. The Abaqus/Standard finite element code calls the Helius:MCT User-Defined Material Subroutine at each Gaussian integration point in the model where constitutive relations or stresses are requested. In Figure 1, the Helius:MCT Composite Material Library is used to store all of the material coefficients that are needed to completely define the MCT multiscale material model for various composite materials. Before a particular composite material can be used in a Helius:MCT-enhanced finite element model, the composite material must undergo MCT material characterization, and a unique material file must be added to the Helius:MCT Composite Material Library. As shown in Figure 1, the Helius:MCT User-Defined Material Subroutine opens and reads the Helius:MCT Composite Material Library to extract the necessary material coefficients for any composite materials that are used in the finite element model. Note that material libraries are not necessary for Helius:MCT cohesive materials. Since the number of inputs required to define a cohesive material are much less than a composite, the entire material is defined within the Abaqus input file.


Abaqus/StandardHelius:MCTUser-Defined

Material Subroutine

Helius:MCTComposite Material

Library

Abaqus/CAEHelius:MCT

Graphical UserInterface (GUI)

Helius:MCTGraphical UserInterface (GUI)

Abaqus input file

Abaqus/Viewer

Abaqus output file

Figure 1: Schematic diagram of the individual components of the Helius:MCT software and their interaction with the Abaqus/Standard software components

In addition to the software modules depicted in Figure 1, Helius:MCT contains two additional

auxiliary programs: Helius Material Manager and xSTIFF. Helius:Material Manager is a stand-alone program that allows the user to characterize new composite materials and add them to the Helius:MCT Composite Material Library. xSTIFF is a stand-alone program that greatly simplifies the creation of Helius:MCT-compatible Abaqus input files by automatically calculating and inserting any extraneous stiffness parameters that are required by elements that use reduced integration . Note that xSTIFF is not required for analyses that use strictly Helius:MCT cohesive materials.


1.3 Helius:MCT Support Documentation This User’s Guide assumes the reader is familiar with the basic use and concepts of the Abaqus/Standard finite element modeling system, including the following three processes: 1) Creating input files for Abaqus/Standard, 2) Running Abaqus/Standard finite element analyses, and 3) Viewing the results from an Abaqus/Standard finite element analysis. Given this assumption, the purpose of this document is to describe those aspects of creating an Abaqus input file that are unique to finite element analyses that utilize Helius:MCT for enhanced multiscale modeling of fiber-reinforced composite structures. In addition, this document discusses appropriate methods for viewing the enhanced results that are available in the output file when Helius:MCT is used in the finite element analysis. The remainder of this document is organized as follows:

Section 2 This section identifies the Abaqus keyword statements that should be present in an Abaqus input file to achieve compatibility with Helius:MCT and take full advantage of its superior convergence characteristics for nonlinear problems.

Section 3 This section describes the use of Abaqus/CAE to create Abaqus input files that are compatible with Helius:MCT. More specifically, Section 3 describes the use of the Helius:MCT Graphical User Interfaces (GUIs) that are accessed from within Abaqus/CAE.

Section 4 For users who choose to employ a text editor to manually create their Abaqus input files, Section 4 describes the process of manually converting existing Abaqus input files to achieve compatibility with Helius:MCT.

Section 5 For users who want to run Helius:MCT on Linux this section describes the necessary steps to do so.

Section 6 Finally, this section describes each of the enhanced solution variables that are computed by Helius:MCT during a finite element simulation, and describes the use of Abaqus/Viewer to view the enhanced MCT results.

The collective documentation for Helius:MCT is divided into several documents. These documents are listed below along with a brief description of each one.

The installation guide explains the installation of the Helius:MCT software on your computer.

Helius:MCT Installation Guide

The user’s guide is a general reference for using Helius:MCT to provide enhanced composite modeling capabilities for Abaqus/Standard finite element analyses of composite structures.

Helius:MCT User’s Guide


The Material Manager User’s Guide provides step-by-step guidelines for using the Helius Material Manager, a convenient graphical user interface (GUI) for creating a material file required to execute a Helius:MCT analysis.

Helius Material Manager User’s Guide

xSTIFF is a command line program that reads an Abaqus input file and automatically computes and inserts all of the extraneous stiffness parameters that are required by any reduced integration elements that utilize Helius:MCT composite materials. This auxiliary program significantly improves the speed and accuracy of the model building process.

xSTIFF User’s Guide

The Theory Manual provides an in-depth explanation of MCT theory and discusses the various features that are implemented in the Helius:MCT User-Defined Material Subroutine. In addition, the Theory Manual describes the important process of characterizing a composite material for use with the MCT decomposition.

Helius:MCT Theory Manual

These documents are step-by-step tutorials that demonstrate the use of Helius:MCT. The primary emphasis is the creation of Abaqus input files that are compatible with Helius:MCT and the viewing of special solution variables that are computed by Helius:MCT.

Helius:MCT Tutorials 1, 2, 3 and 4

• Tutorial 1 demonstrates the ply-based functionality of Helius:MCT and the use of Abaqus/CAE in building an Abaqus input file .

• Tutorial 2 demonstrates the process of manually converting an existing Abaqus input file to achieve compatibility with Helius:MCT.

• Tutorial 3 demonstrates the use of Abaqus/CAE and Helius:MCT Linear in building an Abaqus input file.

• Tutorial 4 demonstrates the cohesive-based functionality of Helius:MCT and the use of Abaqus/CAE in building an Abaqus input file.

The example problem documents provide examples of how to use the functionality provided by Helius:MCT to execute a finite element analysis of a composite structure.

Helius:MCT Example Problems 1, 2, and 3

• Example Problem 1 details how the mesh density and element type affect a typical composite structure analysis and compares the Helius:MCT progressive failure analysis capabilities with the built in Abaqus composite analysis functionality.

• Example Problem 2 details how to use the pre-failure nonlinearity functionality of Helius:MCT to get the most accurate analysis of a composite structure.

• Example Problem 3 demonstrates the use of temperature dependent material properties and residual thermal stresses.

Tutorials 1 & 2 Include progressive failure functionality

not available in Helius:MCT Linear

Example Problem 2 include pre-failure

nonlinearity not available in

Helius:MCT Linear

Example Problem 1 includes progressive failure analysis that is not available in

Helius:MCT Linear


2 General Requirements for Abaqus Input Files

This section identifies the keyword statements that should be present in an Abaqus input file to ensure complete compatibility with Helius:MCT and to take full advantage of its superior convergence characteristics for nonlinear, progressive failure problems. More specifically, this section explains the need for these keyword statements in terms of the unique characteristics of Helius:MCT. This section does not discuss the formatting requirements of any keyword statement, nor

3 does it discuss any of the

specific options or data of any keyword statement; these issues are covered in Sections and 4.

2.1 Identification and Definition of Helius:MCT Materials If Helius:MCT is used to provide the constitutive relations for a particular composite or cohesive material, then Abaqus/Standard considers the material to be a 'user-defined material type.' Consequently, Abaqus/Standard requires the following three keyword statements for each “user-defined material type” that is used in the finite element model:

1. *MATERIAL, 2. *USER MATERIAL, and 3. *DEPVAR.

A detailed description of each of these keywords and their functionality in Abaqus/Standard can be found in the Abaqus Keywords Reference Manual; however, their use in defining materials for Helius:MCT is briefly described below. The *MATERIAL keyword statement is used to identify the name of the composite or cohesive material. When defining a composite material the name must precisely match the name of a composite material that is stored in the Helius:MCT composite material database. For more information on how to create a material file that can be added to the Helius:MCT composite material database, please refer to the Helius Material Manager User’s Guide. The *USER MATERIAL keyword statement identifies the material as a “user-defined material type.” In addition, the data and options of the *USER MATERIAL keyword statement are used by Helius:MCT to identify the specific type of multiscale constitutive relations that should be used for the material. The *DEPVAR statement is used to request storage space within Abaqus/Standard for the MCT state variables that must be tracked at each integration point in the model. The specific data and options of the *MATERIAL, *USER MATERIAL, and *DEPVAR keyword statements (along with their formatting requirements) are discussed in Sections 3 and 4. For now, it suffices that the reader is aware that the *MATERIAL, *USER MATERIAL, and *DEPVAR keyword statements will be used collectively to identify each of the composite materials that will be processed by Helius:MCT and to identify the specific form of the multiscale constitutive relations that will be used for each of the composite materials.


Nonlinear solution control parameters are not required for simulations using

Helius:MCT Linear

2.2 Definition of Extraneous Stiffness Parameters for Certain Types of Elements Certain types of Abaqus elements (e.g., shell elements and reduced integration elements) require extraneous stiffness parameters in order to stabilize their response to deformation modes whose stiffness is not provided by material constitutive relations. Depending on the specific type of element, these extraneous stiffness parameters may include one or more of the following: transverse shear stiffnesses, hourglass control stiffnesses, thickness modulus, and thickness Poisson ratio. Provided that the finite element model uses only standard Abaqus material types, Abaqus/Standard will automatically compute all of the required extraneous stiffness parameters at runtime. However, when the finite element model contains user-defined material types, Abaqus/Standard cannot automatically compute all of the extraneous stiffness parameters that are required. In that case, the Abaqus input file must explicitly define any required extraneous stiffness parameters. These extraneous stiffness parameters are defined as options or data in the various section keyword statements (e.g., *SOLID SECTION, *SHELL SECTION, etc.). Please refer to Appendix C.1 of this User's Guide for a description of the extraneous stiffness parameters that are required for various element types. In earlier versions Helius:MCT, the calculation of these extraneous stiffness parameters and their insertion in the Abaqus input file required a rather cumbersome manual procedure that is described in detail in Appendices C.2-C.4 of this User's Guide. However, Helius:MCT now includes a new auxiliary program (xSTIFF) that automatically calculates and inserts the required extraneous stiffness parameters into the Abaqus input file. The use of xSTIFF is highly recommended as it greatly accelerates the model building process, while at the same time minimizing the chance for errors to be introduced into the input file. For more information on using xSTIFF to automatically calculate and insert the required extraneous stiffness parameters into the Abaqus input file, please refer to the xSTIFF User’s Guide. Note that extraneous stiffness parameters are not required for cohesive sections, so running xSTIFF is not required for analyses that strictly use Helius:MCT cohesive materials.

2.3 Nonlinear Solution Control Parameters for Helius:MCT It is a widely accepted notion that good convergence (or any convergence at all) is difficult to achieve in a progressive failure simulation of a composite structure. In fact, many progressive failure simulations terminate early, not due to global structural failure, but rather due to the inability of the finite element code to obtain a converged solution at a particular load increment. Helius:MCT significantly improves the overall convergence rate and robustness of finite element simulations of progressive failure of composite structures. Experienced users of Abaqus/Standard are no doubt familiar with the code’s tendency to reduce (or cut-back) the time increment size when the code senses that convergence is difficult to achieve. However, when Helius:MCT is used in conjunction with Abaqus/Standard to perform a progressive failure analysis, the increased robustness of the solution greatly diminishes the need for time incrementation reductions (or cut-backs), thus the analysis can be completed much faster than without the use of Helius:MCT. In order to take full advantage of the superior convergence characteristics of Helius:MCT, the user must change some of the default settings that govern the nonlinear solution process used by Abaqus/Standard. These changes can be enacted using the *CONTROLS keyword statement. In Abaqus/Standard, the default settings for the nonlinear solution process are based on the fundamental assumption of the Newton-Raphson algorithm that the nonlinear response of the composite structure is sufficiently smooth at both the local and global levels. However, in a progressive failure


simulation of a composite structure, the nonlinear response of the composite structure is not

smooth, especially at the local level, and it is this situation that is primarily responsible for the difficulty in obtaining convergence. Helius:MCT is specifically designed to efficiently handle this localized ”jagged” material response; however, the default settings of Abaqus/Standard must be changed in order to allow Helius:MCT to improve the convergence characteristics of the finite element simulation. These default settings can be changed via the data line of the *CONTROLS keyword statement. In this case, the data line of the *CONTROLS keyword statement is used to significantly increase the number of equilibrium iterations that Abaqus/Standard will perform before the code evaluates the need for a reduction (or cut-back) in time step size.

The specific data and options that are used with the *CONTROLS keyword statement is discussed in Sections 3.4 and 4.5. For now, it suffices that the reader is aware that the *CONTROLS keyword statement is used to provide Helius:MCT with the freedom to drastically improve the speed and robustness of convergence in progressive failure simulations.

2.4 Requesting Output of Solution Variables that are Unique to Helius:MCT Helius:MCT calculates a number of specialized state variables that define the constituent average stress and strain fields, in addition to the damage state of the composite material. These state variables are stored by Abaqus/Standard at each individual integration point within the finite element model. To allow these state variables to be examined in Abaqus/Viewer, the Abaqus input file must explicitly identify the state variables that will be written in the Abaqus output file. This request is made via the data lines of the *ELEMENT OUTPUT keyword statement. Specific usage and formatting of the *ELEMENT OUTPUT keyword statement are discussed in Sections 3 and 4. For now, it should be understood that the *DEPVAR and the *ELEMENT OUTPUT keywords allow the user to request which solution dependent state variables should be available for post-processing. Appendices D and E of this User's Guide contains a detailed description of each of the MCT state variables for composite and cohesive materials.


3 Using Abaqus/CAE To Create Abaqus Input Files For Use With Helius:MCT

Section 3 describes the use of Abaqus/CAE to create an Abaqus input file that is completely compatible with Helius:MCT. It is assumed that the reader is familiar with the process of using Abaqus/CAE to create an Abaqus input file. Consequently, this section focuses primarily on those aspects of model creation that are unique to models utilizing Helius:MCT. In particular, this section explains the use of the two Helius:MCT Graphical User Interfaces (GUI’s) that can be accessed from within Abaqus/CAE. The Helius:MCT Ply GUI provides a simple, intuitive means for the user to create composite material definitions that are compatible with Helius:MCT. The Helius:MCT Cohesive GUI allows the user to create cohesive material definitions for delamination predictions in Helius:MCT.

3.1 Creating Composite Materials with the Helius:MCT Ply GUI Each composite material that is processed by Helius:MCT is considered by Abaqus/Standard to be a user-defined material type. The Helius:MCT Ply GUI provides a simple means of creating these composite material definitions in the Abaqus input file. Helius:MCT Ply allows the user to select a composite material from the Helius:MCT composite material database and then select a number of different options for the multiscale constitutive relations that will be used to define the thermomechanical response of the composite material. To open the Helius:MCT Ply GUI from within Abaqus/CAE, go to the main toolbar and select Plug-ins Helius:MCT - Ply. The GUI will appear as shown in Figure 2.


Figure 2: The Helius:MCT Ply Graphical User Interface (GUI)

As shown in Figure 2, there are sixteen possible steps involved in using the Helius:MCT Ply GUI to define a composite material type for Helius:MCT. Each of the fifteen steps is discussed below.

1 2 3 4

5 6 7 8 9 10 11

12

15 16

13 14


1. Composite Material Selection – The user selects a composite material from the Helius:MCT material library. If the material library does not contain a composite material that the user would like to use in an analysis, a material data file must first be created and added to the material library (refer to Helius Material Manager User’s Guide). Once a composite material is selected, the homogenized (or composite average) engineering constants for that material will be displayed in the box labeled “Engineering Constants for Your Selected Composite”. These constants are displayed in Helius:MCT’s default system of units (N/m/K). To display these constants in a different coordinate system, the user may select a different system of units (see step 2).

2. System of Units – The user selects the system of units that should be used by Helius:MCT to

compute constitutive relations and stresses. By default, Helius:MCT expresses constitutive relations and computes stress in the (N/m/K) system of units. If the finite element model is created using a different system of units, then Helius:MCT must convert its constitutive calculations to the system of units required by the finite element model. For such purposes, Helius:MCT contains conversion factors for four commonly used systems of units: N/m/K, N/mm/K, lb/in/R, and lb/ft/R. If the finite element model uses one of these four systems of units, the user must select the appropriate system from the drop-down list. In the event that the finite element model’s system of units does not appear in the drop-down list, the user should select the default system of N/m/K and then refer to Appendix A.1 for details on how to manually modify the Abaqus input file to utilize a custom system of units. The reader can also refer to Appendix A.1 for more detailed information on systems of units in general.

3. Principal Material Coordinate System – Helius:MCT expresses constitutive relations and

computes stresses in the principal material coordinate system of the composite material. Here the user selects one of two or three possible orientations for the composite’s principal material coordinate system.

For Unidirectional Microstructures

: Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fiber direction, while the ‘2’ and ‘3’ directions lie in the material’s plane of transverse isotropy. This default orientation of the principal material coordinate system corresponds to the selection of "1" from the fiber direction drop down menu. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fiber direction, while the ‘1’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy. This particular orientation of the principal material coordinate system corresponds to the selection of "2" from the fiber direction drop down menu. If the user selects the value ‘2’ from the drop-down list, the Helius:MCT GUI updates the contents of the display box labeled “Engineering Constants for Your Selected Composite”.

For Woven Microstructures: Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fill tow direction, while the ‘2’ direction corresponds to the warp tow direction, and the ‘3’ direction corresponds with the out-of-plane direction. This default orientation of the principal material coordinate system corresponds to the selection of "1" from the fiber direction drop down menu. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fill tow direction, while the ‘1’ direction corresponds to the warp tow direction. This particular orientation of the principal material coordinate system corresponds to the selection of "2" from the fiber direction drop down menu. Additionally, the user may change the


Steps 5, 6, 7, 8, 9, 10, 12 and 13 listed below do not apply to Helius:MCT Linear

orientation of the principal material coordinate system so that the ‘3’ direction is aligned with the fill tow direction while the ‘2’ direction corresponds to the warp tow direction. This particular orientation of the principal material coordinate system corresponds to the selection of "3" from the fiber direction drop down menu.

For more information on the orientation of principal material coordinate systems, please refer to Appendix A.2.

4. Temperature Dependence – (unidirectional composites only) If a list of temperatures is

displayed, then the material data file for the selected material contains material properties at multiple temperatures. After selecting a temperature, the properties that are stored for that temperature are displayed in the “Engineering Constants for Your Selected Composite”. During a finite element analysis, Helius:MCT linearly interpolates the composite and constituent properties for any given temperature that lies within the bounds of the lowest and highest temperature points stored in the material file. For temperatures below the lowest stored temperature datum, Helius:MCT will use the material properties stored at the lowest temperature datum (Helius will not extrapolate properties beyond the bounding stored temperature data points). The same is true for temperatures above the highest stored temperature datum. For further information on the use of temperature dependent material properties in Helius:MCT, please refer to section 9 of the Helius:MCT Theory Manual. For further information on adding a new temperature dependent material to the Helius:MCT material library, please refer to the Helius:MCT Material Manager User’s Guide.

5. Progressive Failure - The user chooses whether or not to perform a Progressive Failure

Analysis. If the user checks this box, then Helius:MCT will routinely evaluate both the matrix failure criterion and the fiber failure criterion to determine if either constituent has failed. Each constituent failure criterion is based on the corresponding constituent average stress state. In the event that one or both of the constituents fail, the stiffness of the failed constituent(s) and the stiffness of the composite are appropriately reduced instantaneously. It should be emphasized that an instantaneous reduction of the stiffness of a failed constituent effectively results in a discontinuous, piecewise linear stress/strain response for the constituent and the composite. However, when this type of discrete material response is applied independently at each of the integration points in a large finite element model, the net result is a gradual (or progressive) degradation of the overall stiffness of the composite structure (hence the name Progressive

Failure Analysis).

The progressive failure analysis feature is the foundation component of Helius:MCT’s nonlinear multiscale constitutive relations. Other aspects of material nonlinearity can be invoked (as shown in steps 6, 7 and 8); however, these additional forms of nonlinearity cannot be activated unless the progressive failure analysis feature is also activated. Consequently, if the user chooses not to check the progressive failure analysis box, then Helius:MCT will use linear elastic constitutive relations. For further information on progressive failure analyses and constituent failure criteria, refer to Appendix A.3 of this User's Guide and Section 4 of the Helius:MCT Theory Manual.


6. Calculate Failed Plain Weave Properties - (plain weave composites only) Selecting this option will force Helius:MCT to calculate the failed plain weave properties using the matrix and fiber degradation levels specified in steps 11 and 12. If this option is not selected, the failed material properties that were calculated when the material data file was created using Helius:Material Manager are used. For example, if the matrix degradation value was 0.7 and the fiber degradation value was 0.015 when the material was created (using Helius Material Manager) and this option is unselected, the failed material properties corresponding to a matrix degradation of 0.7 and a fiber degradation of 0.015 are used. If, on the other hand, this option is selected and, for example, the user specifies a matrix degradation of 0.8 and a fiber degradation of 0.001 in steps 11 and 12, then the failed material properties corresponding to a matrix degradation of 0.8 and a fiber degradation of 0.001 are used. Note: The matrix degradation for woven lamina is recommended to be not less than 0.7.

7. Hydrostatic Strengthening of the Composite – (unidirectional composite only) The user chooses whether or not to account for the experimentally observed strengthening of the composite in the presence of a hydrostatic compressive stress. If the user checks this box, then Helius:MCT will monitor the hydrostatic compressive stress level in the matrix constituent. If the hydrostatic compressive stress level in the matrix constituent exceeds a threshold value, then the strength of both the matrix constituent and the fiber constituent are scaled upwards commensurate with the level of hydrostatic compressive stress level in the matrix constituent. For further information on Hydrostatic Strengthening of the Composite, refer to Appendix A.6 of this User's Guide and Section 7 of the Helius:MCT Theory Manual.

8. Energy-Based Degradation – (unidirectional composites only) The user chooses whether or not

to use an Energy-Based approach to degrade composite stiffness as a function of increasing strain. If the user checks this box, then Helius:MCT will employ a piecewise linear degradation of composite stiffness after a failure event, while conserving the total energy supplied by the user. The type of failure event (i.e. fiber or matrix failure) determines which composite stiffnesses are reduced linearly with increasing strain. In this case, the constituent failure criteria are assumed to simply identify the onset of a failure event. As the deformation of the lamina continues to increase, the stiffness of the composite is subject to a series of discrete reductions until the stiffness of the composite finally reaches its minimal level indicating complete failure of the constituent. It is of importance to note a consistent set of material properties is enforced between the microscopic and macroscopic scales to allow for the composite material properties to degrade along with the matrix after the matrix constituent fails. For instance, a matrix failure event will result in a linear degradation of composite Ec

22, Ec33, G

c12, G

c13 and Gc

23, while also degrading matrix Em

11, Em22, E

m33, G

m12, G

m13 and Gm

23. However, a fiber failure event will result in a linear degradation of composite Ec

11, Gc12 and Gc

13

, but the constituents are no longer degraded as the stresses and strains in the constituents are no longer useful. It should be emphasized that this feature and Post-Failure Nonlinearity are mutually exclusive for all analyses. For further information on Energy-Based degradation and its impact on analyses, refer to Appendix A.5 of this User's Guide and the Helius:MCT Theory Manual.

9. Pre-Failure Nonlinearity – (unidirectional composites only) The user chooses whether or not to account for the nonlinear longitudinal shear stress/strain response that is commonly observed in fiber-reinforced composite materials. If the user checks this box, then Helius:MCT will employ a four-segment, piecewise linear representation of the longitudinal shear stress/strain response


(i.e., σc12 vs. ε

c12, and σc

13 vs. εc13

), while the responses of the other four stress and strain components remain unaffected by this feature. The entire series of three discrete reductions in the longitudinal shear moduli of the composite is conducted in such a way that the piecewise linear longitudinal shear response closely matches experimentally measured longitudinal shear data for the composite.

It should be emphasized that this feature is only available for those unidirectional composite materials where a longitudinal shear stress/strain curve was supplied during the MCT material characterization process. If this feature is requested for a composite material that was characterized without a longitudinal shear stress/strain curve, then Helius:MCT will issue an error message at runtime and execution will halt. For further information on the Pre-Failure Nonlinearity feature, refer to Appendix A.4 of this User's Guide, Section 5 of the Helius:MCT Theory Manual, and Example Problem 2. For further information on characterizing new composite materials with Pre-Failure Nonlinearity capability, please refer to the Helius:MCT Material Manager User’s Guide.

10. Post-Failure Nonlinearity – (unidirectional composites only) The user chooses whether or not to

account for the support that is provided to a failed lamina by the surrounding un-failed lamina. When individual matrix cracks appear in a lamina, the surrounding undamaged lamina are able (via interlaminar shear stresses) to divert the load path around the individual matrix cracks and back into the failed lamina. The net result of this process is that matrix failure in a lamina is not a discrete catastrophic event, rather it is a gradual process marked by a gradual increase in the density of matrix cracks. In this case, the matrix failure criterion is assumed to simply identify the onset of matrix crack development. As the deformation of the lamina continues to increase, the stiffness of the matrix constituent is subject to a series of discrete reductions until the stiffness of the matrix constituent finally reaches its minimal level indicating complete matrix failure (i.e., matrix crack saturation). It is of importance to note a consistent set of material properties is enforced between the microscopic and macroscopic scales to allow for the composite material properties to degrade along with the matrix.

It should be emphasized that this feature is only available for those unidirectional composite materials where the transverse normal failure strain was supplied during the MCT material characterization process. If this feature is requested for a composite material that was characterized without a transverse normal failure strain, then Helius:MCT will issue an error message at runtime and execution will halt. This feature is also mutually exclusive with the Energy-Based Degradation option discussed above. For further information on the Post-Failure Nonlinearity feature, refer to Appendix A.5 of this User's Guide and Section 6 of the Helius:MCT Theory Manual. For further information on characterizing new composite materials with Post-Failure Nonlinearity capability, please refer to the Helius:MCT Material Manager User’s Guide.

11. Residual Stresses – (applicable to unidirectional composites only) This option is used to specify whether or not to explicitly account for thermal residual stresses in the response of the composite material. If this option is checked, then Helius:MCT computes the ply-level and constituent-level thermal residual stresses that are caused by the post-cure cool down from the stress-free temperature displayed under “Engineering Constants for Your Selected Composite” to ambient temperature (defaults to 72.5°F = 22.5°C = 295.65°K). In this case, these ply-level and constituent-level thermal residual stresses will be present prior to the application of any external mechanical and/or thermal loads that are imposed during the simulation. If the user chooses to explicitly account for thermal residual stresses in the analysis, then the user should verify that the


stress-free temperature (synonymous with cure temperature) displayed under “Engineering Constants for Your Selected Composite” is indeed a reasonable value; otherwise, the predicted thermal residual stresses could be quite erroneous.

If this option is not checked for a particular composite material, then thermal residual stresses are not

included in the response of that particular composite material during the simulation. In this case, the stress free temperature of the composite material defaults to Tsf =0° (regardless of the system of units employed), and the temperature change that is used in the constitutive relations [σ = C(ε−α∆T)] is simply computed as ∆T = T − Tsf = T. Several points should be emphasized here. First, the stress free temperature Tsf defaults to 0° even if the composite material data file (Mdata file) explicitly defines a non-zero stress free temperature. Second, regardless of the system of units that are employed by the finite element model, the current temperature T completely defines the temperature change ∆T that is used in the constitutive relations. Third, for composite materials that are characterized at multiple temperatures, the current temperature T will be used to interpolate the various material properties that contribute to the constitutive relations; consequently, it is recommended that a single-temperature characterization (i.e., a single-temperature Mdata file) should be used for the composite material in question. In summary, if the user does not request this option, then the current temperature T influences Eqs. 10.1 of the Theory Manual in two different ways: 1) the temperature change used in the constitutive relations simply becomes ∆T=T, and 2) T is used to interpolate the temperature-dependent material properties that contribute to the constitutive relations. Refer to Section 10 of the Helius:MCT Theory Manual for further information on the thermal residual stresses formulation used by Helius:MCT.

It should be emphasized that the default temperature in Abaqus/Standard is 0°. This default temperature is completely compatible with the default stress free temperature of 0° that is assumed when the seventh user material constant is specified as 0. In this case, the model can still be subjected to temperature changes by simply imposing a temperature other than 0°; however, these thermal stresses develop over the course of the analysis, as opposed to being present at the start of the analysis.

12. Matrix Post-Failure Stiffness / Matrix Degradation Energy – For analyses not using Energy-Based Degradation, this value is a fraction that is used to define the damaged elastic moduli of the matrix constituent after matrix constituent failure occurs. Specifically, the value is the ratio of the failed matrix constituent moduli to the unfailed matrix constituent moduli. A value of 0.1 would mean that after a matrix failure occurs at an integration point, all six of the matrix constituent moduli (Em

11, Em22, E

m33, G

m12, G

m13, G

m23

) are reduced to 10% of the original undamaged matrix constituent moduli. The matrix post-failure stiffness value must be greater than 0, and less than or equal to 1. By default, the matrix post-failure stiffness value is set to 0.1. If the post-failure nonlinearity feature is turned on, this value will be ignored.

For analyses using Energy-Based Degradation, this value is the total energy dissipated before and after a matrix failure assuming a linear degradation of composite stiffness after a failure event. Specifically, composite Ec

22, Ec33, G

c12, G

c13, G

c23

are degraded after a matrix failure event according to this energy, the composite stress state at fiber failure and the volume of the element. For more information on the computation of the energy values, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual.


13. Fiber Post-Failure Stiffness / Fiber Degradation Energy – For analyses not using Energy-Based Degradation, this value is a fraction that is used to define the damaged elastic moduli of the fiber constituent after fiber constituent failure occurs. Specifically, the value is the ratio of the failed fiber constituent moduli to the unfailed fiber constituent moduli. A value of 0.01 would mean that after a fiber failure occurs at an integration point, all six of the fiber constituent moduli (Ef

11, Ef22, E

f33, G

f12, G

f13, G

f23

) are reduced to 1% of the original undamaged fiber constituent moduli. The fiber post-failure stiffness value must be greater than 0, and less than or equal to 1. The default value of the fiber post-failure stiffness is automatically set to 1E-06.

For analyses using Energy-Based Degradation, this value is the total energy dissipated for a fiber failure assuming a linear degradation of composite stiffness before and after a fiber failure event. Specifically, composite Ec

11, Gc12, and Gc

13

are degraded linearly after a fiber failure event according to this energy, the composite stress state at fiber failure, and the volume of the element. For more information on the computation of the energy values, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual.

14. Average Element Thickness – (unidirectional composite only) If Energy-Based Degradation is selected for unidirectional materials, this value represents the average thickness of the three-dimensional elements assigned to the material, where the thickness is measured through the thickness of the laminate. For two-dimensional elements (i.e. shells, plane stress), this value should be set to 1.0.

15. Output Constituent Average Stress and Strain States – The user chooses whether or not to output the fiber average stress and strain fields and the matrix average stress and strain field to the output database file (.odb file). If the user checks this box for a unidirectional composite, then the number of MCT state variables output to the .odb file increases from 6 to 34 (10 to 34 if Energy-Based Degradation is requested). If the user checks this box for a woven composite, then the number of MCT state variables output to the .odb file increases from 6 to 90. Printing these extra state variables increases the total run time slightly and significantly increases the size of the .odb file. Thus, this option should only be selected if the constituent average stress and strain states are of interest to the user.

16. Name State Dependent Variables – The user chooses whether or not to allow the Helius:MCT GUI to re-name the first 6 MCT state variables (or 10 if Energy-Based Degradation is requested). If the user checks this box, then the first 6 MCT state variables will be re-named from their Abaqus default names (SDV1, SDV2, …, SDV6) to descriptive names. See Appendix D for a complete description of each of the MCT state variables.

Warning: Invoking this feature might cause Abaqus/CAE to produce input files that contain conflicting keywords. See Appendix F for a description of this problem and the suggested method of resolving this issue.

After completing steps 1 through 16, the user should click the OK button on the Helius:MCT GUI to create a user-defined composite material that is compatible with Helius:MCT. Once the OK button is clicked, a new material will be created and the appropriate Abaqus keyword statements are created for the new user-defined composite material. The newly created Abaqus keyword statements (*MATERIAL, *DEPVAR, and *USER MATERIAL) can be viewed in the Keywords Editor. To access the Keywords Editor from the main toolbar, select Model Edit Keywords “Name of Model”. Figure 3 shows an example of the Keyword Editor containing the *MATERIAL, *DEPVAR, and *USER MATERIAL


keyword statements. The following list describes each of the Abaqus keyword statements that are shown in Figure 3.

• *Material, name=IM7_8552 creates a material and assigns it the name IM7_8552. Note that the name IM7_8552 was selected via Step 1 from the pull-down list of materials in the Helius:MCT composite material database.

• *DepVar creates storage space for 6 MCT state variables that Abaqus/Standard will track at each

integration point in the finite element model. If the user had requested output of the constituent average stress and strain states via Step 12, the number of MCT states variables would increase to 34. Note that each of the 6 MCT state variables is being re-named; for example, SDV1 is re-named MAT_STATE, and SDV2 is re-named FI_MATRIX. This re-naming is only present in the *DEPVAR statement if the user checks the Name State Dependent Variables box via Step 15. Otherwise, the Abaqus default names will be used (SDV1, SDV2, …, SDV6).

• *User Material, constants=13 identifies the material as a user-defined material that employs 13

different constants to specify information needed in the definition of the material. The values of these 13 constants are listed in the data line as 1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.1, 0.01. These constants (referred to as user material constants) are used by the Helius:MCT User-Defined Material Subroutine to convey the specific choices made by the user in completing Steps 2 through 13 of the Helius:MCT GUI. The thirteen constants, in order, pertain to the system of units, the orientation of the principal material coordinate system, progressive failure analysis, pre-failure nonlinearity, post-failure nonlinearity or energy-based degradation, hydrostatic strengthening, stress free temperature, (constants 8-11 are currently unused), matrix post-failure stiffness or matrix degradation energy, and fiber post-failure stiffness or fiber degradation energy. For user material constants 3, 4, 6, and 7, a value of 1 means the option is ‘on’, and a value of 0 means the option is ‘off’. For user material constant 5, a value of 0 indicates both post-failure nonlinearity and energy-based degradation are turned off, a value of 1 indicates post-failure nonlinearity is turned on, and a value of 2 indicates energy-based degradation is turned on. In this example, the default system of units (N/m/K) is selected; the principal material coordinate system is oriented with the ‘1’ direction aligned with the fiber direction; progressive failure analysis is turned ‘on’, pre-failure nonlinearity is turned ‘off’; post-failure nonlinearity and energy-based degradation are turned ‘off’, hydrostatic strengthening is turned ‘off’, the stress free temperature is set to zero, matrix post-failure stiffness is set to 10%, and fiber post-failure stiffness is set to 1%. Note: Appendix A provides a complete description of each of the user material constants.


Figure 3: Keywords Editor showing the keyword statements that collectively define a Helius:MCT material

3.2 Creating Cohesive Materials with the Helius:MCT Cohesive GUI Each cohesive material that is processed by Helius:MCT is considered by Abaqus/Standard to be a user-defined material type. The Helius:MCT Cohesive GUI provides a simple means of creating these cohesive material definitions in the Abaqus input file. Helius:MCT Cohesive allows the user to fully define the cohesive material including damage initiation and damage evolution parameters. To open the Helius:MCT Cohesive GUI from within Abaqus/CAE, go to the main toolbar and select Plug-ins Helius:MCT - Cohesive. The GUI will appear as shown in Figure 4.


Figure 4: Helius:MCT Cohesive GUI in Abaqus/CAE

As shown in Figure 4, there are fifteen possible steps involved in using the Helius:MCT Cohesive GUI to define a cohesive material type for Helius:MCT. Each of the fifteen steps is discussed below. See Appendix B for a technical discussion of these parameters.

1. Material Name - Enter the name of your material. This name will be displayed under the Materials tree in Abaqus/CAE once the material is added.

2. Normal Stiffness - A number greater than zero which defines the normal stiffness, Knn, of the

cohesive material. Knn relates the normal traction in the cohesive material to the strain as

tn = Knnεn

where tn is the normal traction and εn is the strain in the normal direction (local 3-direction).

1

2 3 4

5 6 7

8 9

10-12 13 14 15


3. First Shear Stiffness - A number greater than zero which defines the first shear stiffness, Kss, of the cohesive material. Kss relates the traction in the local 1-direction in the cohesive material to the strain as

ts = Kssεs

where ts is the first shear traction and εs is the strain in the local 1-direction

4. Second Shear Stiffness - A number greater than zero which defines the second shear stiffness,

Ktt, of the cohesive material. Ktt relates the traction in the local 2-direction in the cohesive material to the strain as

tt = Kttεt

where tt is the second shear traction and εt is the strain in the local 2-direction.

5. Maximum Normal Traction - A number greater than zero which represents the maximum amount of traction the cohesive material can sustain in the normal direction (local 3-direction) before damage initiates, Sn.

6. Maximum First Shear Traction - A number greater than zero which represents the maximum amount of traction the cohesive material can sustain in the local 1-direction before damage initiates, Ss.

7. Maximum Second Shear Traction - A number greater than zero which represents the maximum amount of traction the cohesive material can sustain in the local 2-direction before damage initiates, St.

8. Damage Initiation Criterion - Allows the user to select a maximum traction or quadratic based

damage initiation criterion. The maximum traction criterion defines damage initiation as the point when any of the tractions meet or exceed their corresponding maximum traction value. The quadratic based criterion uses a quadratic interaction of the traction to maximum traction ratios to predict damage initiation.

9. Softening Type - Allows the user to select how damage will evolve after damage initiation. Once

damage initiates in a cohesive material the stiffness of the material decreases as material deformation increases. Eventually, the stiffness of the cohesive material will reduce to zero and the material will no longer sustain any load. For a softening type of "Displacement" see step 10 below, for "Energy" see step 11, and for "Energy (Mixed Mode, Power Law)" see steps 12-15.

10. Displacement At Failure - A number greater than zero which defines the difference between the

effective displacement at complete failure and the effective displacement at damage initiation, δm

f - δmo

.

11. Fracture Energy - A number greater than zero which defines the total energy dissipated due to failure, GC. In mathematical terms, this value is the area under the traction - separation curve.

12. Normal Mode Fracture Energy - A number greater than zero which defines the total energy

dissipated due to failure under a pure normal mode, GnC .


13. First Shear Mode Fracture Energy - A number greater than zero which defines the total energy

dissipated due to failure under a pure first shear mode, GsC

.

14. Second Shear Mode Fracture Energy - A number greater than zero which defines the total energy dissipated due to failure under a second shear normal mode, Gt

C

.

15. Alpha - The exponent used in the mixed mode power law damage evolution equation, α.

3.3 Specifying Extraneous Stiffness Parameters Required by Certain Element Types

Certain types of Abaqus elements (e.g., beam elements, shell elements, and reduced integration elements) require extraneous stiffness parameters in order to stabilize their response against deformation modes that are not governed directly by material constitutive relations. These extraneous stiffness parameters are defined as either options or data in the Section keyword statement that is referenced by the element in question. Depending upon the specific type of element being used, one or more of the following types of extraneous stiffness parameters may need to be specified as part of the Section definition that is referenced by the element.

• Section Poisson Ratio • Section Thickness Modulus • Section Transverse Shear Stiffnesses: Kts

11, Kts22, and Kts

12

• Membrane Hourglass Stiffness Control Parameter

• Bending Hourglass Stiffness Control Parameter Appendix B.1 provides a detailed discussion of each type of extraneous stiffness parameter, in addition to listing the specific extraneous stiffness parameters that are required by each type of element. In earlier versions of Helius:MCT, the calculation of these extraneous stiffness parameters and their insertion in the Abaqus input file required a rather cumbersome manual procedure that is described in detail in Appendices C.2-C.4 of this User's Guide. However, Helius:MCT now includes an auxiliary program (xSTIFF) that automatically calculates and inserts the required extraneous stiffness parameters into the Abaqus input file. The use of xSTIFF is highly recommended as it greatly accelerates the model building process, while at the same time minimizing the chance for errors to be introduced into the input file. With the availability of xSTIFF, the user can now postpone the task of defining the extraneous stiffness parameters until the model building process is completed and an Abaqus input file is saved. xSTIFF can then be run to automatically add any required extraneous stiffness parameters to the saved Abaqus input file. For more information on using xSTIFF to automatically calculate and insert the required extraneous stiffness parameters into the Abaqus input file, please refer to the xSTIFF User’s Guide. Note that if the analyses uses exclusively Helius:MCT cohesive materials (in addition to Abaqus material types), xSTIFF is not required. It is only required for analyses that use Helius:MCT ply materials.


Step modifications referenced below are only applicable to the full version of Helius:MCT as they pertain to

progressive failure simulations.

Note: If the user chooses to manually define the extraneous stiffness parameters, Appendices C.1-C.4 completely describe the processes of identifying the required extraneous stiffness parameters, calculating their values, and inserting the correctly formatted values into the Abaqus input file.

3.4 Step Modifications Helius:MCT significantly improves the overall convergence rate and robustness of finite element

simulations of progressive failure of composite structures. However, in order to take full advantage of the superior convergence characteristics of Helius:MCT, the user must change some of the default settings that govern the nonlinear solution process used by Abaqus/Standard. This section discusses the use of Abaqus/CAE to make the recommended changes to the parameters that govern the nonlinear solution process used by Abaqus/Standard. It is recommended that the user specify the time incrementation parameters that are desired in the progressive failure analysis. Since the use of Helius:MCT provides more robust convergence, it is anticipated that the progressive failure analysis will require far fewer time incrementation reductions (or cut-backs) than would be possible without Helius:MCT. This characteristic may influence the user’s choice of time incrementation parameters. The time incrementation parameters can be specified from the Incrementation Tab in the Edit Step dialog box as shown in Figure 5. There are four settings that can be changed: the maximum allowable number of time increments, the value of the initial time increment, the minimum allowable value of a time increment, and the maximum allowable value of a time increment. For analyses that use Helius:MCT cohesive materials, the Extrapolation parameter should be set to None. This can be set from the “Other” tab shown in Figure 5.


Figure 5: Location of incrementation parameters in the Edit Step dialog box The user also should change some of the default settings that control the nonlinear solution process employed by Abaqus/Standard. These solution control parameters can be changed in the General Solution Controls Editor dialog box. The General Solution Controls Editor dialog box can be accessed from the Step module by clicking Other General Solution Controls Edit “name of step” from the main toolbar. The General Solution Controls Editor dialog box is shown in Figure 6 with the Time Integration Tab selected. In Figure 6, there are two parameters shown with their default values (Io=4 and IR=8). Both of these parameters should be set to the same large value, say 1000 (e.g., Io=1000 and IR=1000). After specifying the values of Io and IR, click the first of the three tabs that are labeled ‘more’. From the list of parameters that appears, the values of IP, IC, IL and IS should each be set to 1000, and the value of IT should be set to 10. The greatly increased values of Io, IR, IP, IC, IL and IS will ensure that Abaqus/Standard can take full advantage of the improved convergence characteristics provided by Helius:MCT. For a complete discussion of the effect that Helius:MCT exerts on the convergence behavior of the finite element solution, see Section 11 of the Helius:MCT Theory Manual.


Figure 6: General Solution Controls Editor dialog box

3.5 Requesting MCT State Variable Output for Composite Materials The solution-dependent MCT state variables are used to track constitutive quantities of interest at each integration point in the finite element model. If the user checked the box labeled “Output Constitutive Stress/Strain” in the Helius:MCT Ply GUI, then 34 MCT state variables are tracked for unidirectional composite materials or 90 MCT state variables are tracked for woven composite materials; otherwise, 6 MCT state variables are tracked for analyses not using energy-based degradation, and 10 MCT state variables are tracked for analyses requesting the use of energy-based degradation. The default naming convention for the solution-dependent MCT state variables is SDVi, where i=1, 2, 3, …, 6 or 10 or 34 or 90. The most useful of the MCT state variables is SDV1 which is used to track the discrete failure state of the composite material at each integration point in the finite element model. The exact interpretation of the discrete values of SDV1 will depend upon the specific set of Helius:MCT material nonlinearity features that are used in the analysis. Appendix D provides a complete description of each of the MCT state variables, including tables that define the interpretation of the discrete values of SDV1 for various combinations of material type and material nonlinearity features invoked. By default, the MCT state variables are not automatically written to the output database file (*.odb file) and must be explicitly requested. Output of the MCT state variables can be requested by the user in


the Edit Field Output Request dialog box, which can be accessed from the Step module by clicking Output Field Output Requests Edit “Name of output request” in the main toolbar. To request MCT state variable output, select the box labeled "SDV, Solution Dependent State Variables" from the scroll-bar list of output variables shown in Figure 7. By default, the field variables (including the MCT state variables) are only output at the bottom and top section points of each layered element. In order to view the field variables within each material ply, additional section points can be specified by entering their values in the text box that is highlighted in Figure 7. As an example, consider a flat composite plate with 4 plies and 3 section points per ply, for a total of 12 section points as shown in Figure 9. If the default section point values are used, only results for points 1 and 12 will available for viewing; the user will not have access to the results for the interior material plies. However, if output is requested for each section point, then the complete solution results for each ply can be viewed.

Figure 7: Locations of SDV and section point output parameters in the Edit Field Output Request dialog box


3.6 Requesting MCT State Variable Output for Cohesive Materials State variables for Helius:MCT cohesive materials are requested in a similar manner to requesting state variables for composite materials (Section 3.5). However, it is slightly less complex since cohesive elements do not contain section points and therefore do not require output to be requested at individual section points. The number of state variables for cohesive materials is always 9. See Appendix E for a list and description of the state variables for Helius:MCT cohesive materials.

3.7 Deleting a Helius:MCT Material Deleting a material is usually accomplished by simply deleting the material from the model tree or the Material Manager. Because a Helius:MCT material is a user-defined material type, Abaqus/CAE will not automatically delete the *USER MATERIAL or *DEPVAR statements that are part of the material definition. In light of this situation, the procedure for deleting a Helius:MCT material from a finite element model is listed below.

1. Delete the material from the model tree or the Material Manager. The Material Manager can be accessed by clicking Material Manager in the main toolbar. To delete the material from the model tree, right click on the material and select Delete.

2. To remove the keywords that are associated with the deleted material, open the Helius:MCT GUI by clicking Plug-ins Helius:MCT from the main toolbar. Helius:MCT will automatically detect that the material has been deleted and a dialog box will appear as shown in Figure 8. Clicking Continue in this dialog box will result in the removal of the *USER MATERIAL and *DEPVAR statements associated with the deleted Helius:MCT material. The Helius:MCT GUI then reloads and appears on the screen.

3. Within the Helius:MCT GUI, the user can now click the Cancel button to dismiss the Helius:MCT GUI.

Figure 8: Keywords conflict dialog box


4 Using a Text Editor to Convert Pre-Existing Abaqus Input Files for Use with Helius:MCT

For those users who choose to employ a text editor to manually create and modify their Abaqus input files, this section describes the process of modifying an existing Abaqus input file to achieve complete compatibility with Helius:MCT.

4.1 Defining a Helius:MCT Composite Material In an Abaqus input file, there are three different keyword statements that collectively define a Helius:MCT user-defined composite material. These three keyword statements are *MATERIAL, *DEPVAR, and *USER MATERIAL. Consider the following lines from an Abaqus input file that completely specify a Helius:MCT user-defined composite material. *MATERIAL, name=IM7_8552 *DEPVAR 6 1, MAT_STATE 2, FI_MATRIX 3, FI_FIBER 4, ETA_SM 5, ETA_NM 6, SIM_O *USER MATERIAL, constants=13 1,1,1,0,0,0,0,0 0,0,0,0.1,0.01 The *MATERIAL keyword denotes the start of the material definition, and the option ‘name=IM7_8552’ is used to specify the name of the composite material. The name ‘IM7_ 8552’ must exactly match the name of a material found in the Helius:MCT composite material database and a name specified in the section definition of the input file. The *DEPVAR keyword is used to identify the number of solution-dependent MCT state variables that must be tracked at each integration point in the finite element model. The number of solution-dependent MCT state variables is specified on the first data line that follows the *DEPVAR statement. In this example, there are 6 solution-dependent MCT state variables. The remaining data lines that follow the *DEPVAR keyword statement are optional and are simply used to assign new names to each of the 6 MCT state variables. For example, MCT state variable 1 is re-named MAT_STATE, and state variable 2 is re-named FI_MATRIX. If these optional name assignments are not present, then the 6 MCT state variables would simply retain their Abaqus defaults names of SDV1, SDV2, SDV3, …, SDV6. Allowable values for the number of MCT state variables requested in the *DEPVAR statement are the minimal set of 6 if energy-based degradation is not requested, 10 if energy-based degradation is requested (only for unidirectional composites), or the full set of 34 for unidirectional composites, or the full set of 90 for woven composites. It is highly recommended that for both unidirectional and woven composites, the minimal set of 6 MCT state variables should be requested in the *DEPVAR statement unless the user desires post-processing access to the constituent average stresses and strains. See Appendix D for a complete description of the different MCT state variables that are available for unidirectional and woven composite materials.


The third material constant, while required is not

utilized in Helius:MCT Linear

and its value will default to zero.

The *USER MATERIAL keyword indicates that the material is a user-defined material type. The option ‘constants=13’ indicates that there are a total of 13 user material constants specified for the material. Collectively, the user material constants are used by the Helius:MCT User-Material Subroutine to determine the precise form of multiscale constitutive relations that will be used for the material. For any given Helius:MCT material, the number of user material constants must be between 3 and 16. The first three user material constants are required for all Helius:MCT materials. The last three user material constants (i.e., the 14th, 15th, and 16th constants) are only required if the finite element model is defined using a custom system of units. User material constants 8-11 are not utilized and should be left blank or set to 0. Appendix A provides a detailed description of each of the nine utilized user material constants, including the range of allowable values for each constant and the impact that each constant has on the multiscale constitutive relations used to represent the material. Each of the nine user material constants typically defined in an analysis incorporating Helius:MCT are listed below along with a brief description. For a more detailed description of any particular user material constant, refer to the appropriate section of Appendix A.

• System of Units – The first user material constant specifies the system of units that should be used by Helius:MCT in computing the constitutive relations and stresses. In the example provided above, the first user material constant has a value of 1, indicating that Helius:MCT should compute the constitutive relations and stresses in its default system of units (N/m/K). There are three other systems of units (2 → N/mm/K, 3 → lb/in/R, and 4 → lb/ft/R) that can be requested via specific values of the first user material constant, in addition to a custom (or user-defined) system of units. For more information on defining custom systems of units or more information on systems of units in general, please refer to Appendix A.1 which provides a detailed discussion of the first user material constant.

• Principal Material Coordinate System – Helius:MCT expresses constitutive relations and

computes stress in the principal material coordinate system of the composite material. The second user material constant specifies the specific orientation of the principal material coordinate system that will be used by Helius:MCT.

• Unidirectional Microstructures: Helius:MCT’s default principal material coordinate

system is oriented with the ‘1’ direction aligned with the fiber direction, while the ‘2’ and ‘3’ directions lie in the material’s plane of transverse isotropy. This default orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 1. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fiber direction, while the ‘1’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy. This alternative orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 2. In general, the numerical value of the second user material constant identifies the specific principal material axis that is aligned with the fiber direction. For more information, refer to Appendix A.2 which provides a detailed discussion of the second user material constant.

• Woven Microstructures: Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fill tow direction, while the ‘2’ direction


corresponds to the warp tow direction and the ‘3’ direction corresponds with the out-of-plane direction. This default orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 1. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fill tow direction, while the ‘1’ direction corresponds to the warp tow direction. This alternative orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 2. Additionally, the user may change the orientation of the principal material coordinate system so that the ‘3’ direction is aligned with the fill tow direction while the ‘2’ direction corresponds to the warp tow direction. This particular orientation of the principal material coordinate system is selected by setting the second user material constant to a value of 3. In general, the numerical value of the second user material constant identifies the specific principal material axis that is aligned with the fill tow direction. For more information, refer to Appendix A.2 which provides a detailed discussion of the second user material constant.

• Progressive Failure Analysis – The third user material constant activates or deactivates

Helius:MCT’s progressive failure analysis feature. If the progressive failure feature is activated, then Helius:MCT will routinely evaluate both the matrix and fiber failure criterion to determine if either constituent material has failed. Each constituent failure criterion is based on the corresponding constituent average stress state. In the event that one or both of the constituents fail, the stiffnesses of the failed constituent(s) and the stiffnesses of the composite are appropriately reduced to the respective post-failure stiffnesses. It should be emphasized that the progressive failure analysis feature is the foundation component of Helius:MCT’s nonlinear multiscale constitutive relations. Other aspects of material nonlinearity can be invoked via the 4th, 5th and 6th user material constants; however, these additional forms of nonlinearity cannot be activated unless the progressive failure analysis feature is also activated. For more information on the progressive failure analysis feature, refer to Appendix A.3 of this document and Section 4 of the Helius:MCT Theory Manual.

• Unidirectional Microstructures: A value of 1 activates the progressive failure analysis

feature, while a value of 0 deactivates the progressive failure analysis feature.

• Woven Microstructures: A value of 0 deactivates the progressive failure feature, a value of 1 activates the progressive failure feature and uses the matrix and fiber degradation levels from the material data file to calculate the failed material properties, and a value of 2 activates the progressive failure feature and uses the matrix and fiber degradations levels specified by the twelfth and thirteenth user material constants to calculate the failed material properties. Selecting a value of 2 for plain weaves will add approximately 45-60 seconds to the pre-processing time per woven material. A value of 1 will not add run-time during pre-processing because the failed material properties (at the matrix and fiber degradation levels specified during material creation in Helius Material Manager) are already stored in the material file.

• Pre-Failure Nonlinearity (optional, for unidirectional composites only) – The fourth user

material constant activates or deactivates Helius:MCT’s Pre-Failure Nonlinearity feature. A value of 1 activates the pre-failure nonlinearity feature, while the default value of 0 deactivates the pre-failure nonlinearity feature. If the pre-failure nonlinearity feature is activated, then


Helius:MCT will explicitly account for the nonlinear longitudinal shear stress/strain response that is typically observed in unidirectional fiber-reinforced composite materials. The Pre-Failure Nonlinearity feature imposes a series of discrete reductions in the longitudinal shear stiffness of the matrix constituent material, causing the composite material’s nonlinear longitudinal shear response to closely match experimentally measured data. It should be emphasized that the Pre-Failure Nonlinearity feature only affects the longitudinal shear moduli of the composite (i.e., σc

12 vs. εc12, and σc

13 vs. εc13

), while the responses of the other four composite stress and strain components remain unaffected by this feature. Also, the Pre-Failure Nonlinearity feature will not alter the shear stress level at which the composite fails; however, it will result in an overall increase in longitudinal shear deformation of the composite prior to failure. For further information on the Pre-Failure Nonlinearity feature, refer to Appendix A.4 of this document and Section 5 of the Helius:MCT Theory Manual.

Note: The Pre-Failure Nonlinearity feature is only available for unidirectional composite materials. The fourth user material constant is ignored by woven composites.

• Post-Failure Nonlinearity and Energy-Based Degradation (optional, for unidirectional

composites only) – The fifth user material constant activates or deactivates Helius:MCT’s Post-Failure Nonlinearity feature or Helius:MCT’s Energy-Based Degradation feature. A value of 1 activates the Post-Failure Nonlinearity feature, a value of 2 activates the Energy-Based Degradation feature, and the default value of 0 deactivates both the Post-Failure Nonlinearity and Energy-Based Degradation features.

• Post-Failure Nonlinearity: If the Post-Failure Nonlinearity feature is activated, then Helius:MCT will gradually reduce the stiffness of the matrix constituent moduli to their minimum values. When the Post-Failure Nonlinearity feature is activated, the matrix failure criterion simply identifies the initiation of the matrix failure process (or the initiation of matrix cracking). After the matrix failure criterion is triggered, the matrix constituent stiffness is gradually reduced via a series of discrete stiffness reductions that are applied as the matrix average strain state continues to increase beyond the level present at failure initiation. For further information on Post-Failure Nonlinearity, refer to Appendix A.5 of this document and Section 6 of the Helius:MCT Theory Manual.

• Energy-Based Degradation: If the Energy-Based Degradation feature is activated, then

Helius:MCT will gradually reduce the stiffness of the composite moduli to their minimum values in a linear fashion after a failure event has been detected while conserving the energy given in the twelfth and thirteenth user material constants. If three-dimensional elements are used with Energy-Based Degradation, the eleventh user material constant represents the average thickness of the three-dimensional elements. When the Energy-Based Degradation feature is activated, the constituent failure criteria simply identify the initiation of the constituent failure process. After a failure criterion is triggered, the composite stiffness is gradually reduced via a series of discrete stiffness reductions that are applied as the composite strain state continues to increase beyond the level present at failure initiation. The specific stiffness that is affected depends entirely on the constituent failures that have been triggered. For further information on Energy-Based Degradation, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual.


Note: Both the Post-Failure Nonlinearity and Energy-Based Degradation features are only available for unidirectional composite materials. The fifth user material constant is ignored by woven composites.

Note: The Post-Failure Nonlinearity and Energy-Based Degradation features are mutually

exclusive. Note: The Post-Failure Nonlinearity feature is only available for those unidirectional

composite materials where the transverse tensile failure strain ( εult22

) was supplied during the MCT material characterization process. If this feature is requested for a composite material that was characterized without a transverse tensile failure strain, then Helius:MCT will issue an error message at runtime and execution will halt. For more information on the MCT material characterization process, please refer to the Helius Material Manager User’s Guide.

Note: If the Post-Failure Nonlinearity feature is turned on, then the matrix post-failure stiffness value (the twelfth user material constant) is ignored.

Note: If the Energy-Based degradation feature is turned on, then the twelfth and thirteenth

user material constants represent the energies dissipated for a matrix and fiber failure, respectively.

Note: If the Energy-Based degradation feature is turned on, the minimum number of

solution-dependent MCT state variables must be increased from 6 to 10. • Hydrostatic Strengthening (optional, for unidirectional composites only) – The sixth user

material constant activates or deactivates Helius:MCT’s hydrostatic strengthening feature. A value of 1 activates the hydrostatic strengthening feature, while the default value of 0 deactivates the hydrostatic strengthening feature. If the hydrostatic strengthening feature is activated, then Helius:MCT explicitly accounts for the experimentally observed strengthening of the composite in the presence of a hydrostatic compressive stress. If the hydrostatic compressive stress in the matrix constituent exceeds a threshold value, then the strength of both the matrix constituent and the fiber constituent are scaled upwards commensurate with the level of hydrostatic compressive stress level in the matrix constituent. For further information on the hydrostatic strengthening feature, refer to Appendix A.6 of this document and Section 7 of the Helius:MCT Theory Manual.

Note: The Hydrostatic Strengthening feature is only available for unidirectional composite materials. The sixth user material constant is ignored by woven composites.

• Thermal Residual Stress (optional, for unidirectional composites only) – The seventh user

material constant (0 or 1) is used to specify whether or not to explicitly account for thermal residual stresses in the response of the unidirectional composite material. If the seventh user material constant is specified as 1, then Helius:MCT computes the ply-level and constituent-level thermal residual stresses that are caused by the post-cure cool down from the stress-free temperature (i.e. cure temperature) to ambient temperature. In this case, the stress free temperature is read from the material data file (Mdata file) and ambient temperature corresponds to 72.5°F, 22.5°C or 295.65°K. If the seventh user material constant is specified as 1, ply-level and constituent-level thermal residual stresses will be present in the composite material prior to


the application of any external mechanical and/or thermal loads that are imposed during the actual simulation. If the user chooses to explicitly account for thermal residual stresses in the analysis, then the user should verify the material data file (Mdata file) actually contains a defined stress free temperature; otherwise, the stress free temperature will default to 0° and the predicted thermal residual stresses will be quite erroneous. If the seventh user material constant is specified as the default value of 0, then thermal residual stresses are not

included in the response of that particular composite material during the simulation. In this case, the stress free temperature of the composite material defaults to Tsf =0° (regardless of the system of units employed), and the temperature change that is used in the constitutive relations [σ = C(ε−α∆T)] is simply computed as ∆T = T − Tsf = T. Several points should be emphasized here. First, the stress free temperature Tsf defaults to 0° even if the composite material data file (Mdata file) explicitly defines a non-zero stress free temperature. Second, regardless of the system of units that are employed by the finite element model, the current temperature T completely defines the temperature change ∆T that is used in the constitutive relations. Third, for composite materials that are characterized at multiple temperatures, the current temperature T will be used to interpolate the various material properties that contribute to the constitutive relations; consequently, it is recommended that a single-temperature characterization (i.e., a single-temperature Mdata file) should be used for the composite material in question. In summary, if the user does not request this option, then the current temperature T influences the constitutive relations in two different ways: 1) the temperature change used in the constitutive relations simply becomes ∆T=T, and 2) T is used to interpolate the temperature-dependent material properties that contribute to the constitutive relations.

It should be emphasized that the default temperature in Abaqus/Standard is 0°. This default temperature is completely compatible with the default stress free temperature of 0° that is assumed when the seventh user material constant is specified as 0. In this case, the model can still be subjected to temperature changes by simply imposing a temperature other than 0°; however, these thermal stresses develop over the course of the analysis, as opposed to being present at the start of the analysis.

• User Material Constants 8-10 are not used and should be set to 0 or left blank.

• Average Element Thickness – For analyses using Energy-Based Degradation, this value represents the average element thickness of the three-dimensional (i.e. solid) elements associated with the material. The average element thickness is used with solid elements to compute a representative element length that represents the area of the element in the plane of a lamina. For two-dimensional elements (i.e. shell elements and plane stress elements), this value is ignored, and should be entered as 1.0.

Note: The Average Element Thickness is only available for analyses using Energy-Based Degradation. For analyses not using Energy-Based Degradation this value is ignored.

Note: The Average Element Thickness is only available for unidirectional composite

materials. The eleventh user material constant is ignored by woven composites.

• Matrix Post-Failure Stiffness / Matrix Degradation Energy – For analyses not using Energy-Based Degradation, the twelfth user material constant is a fraction that is used to define the


damaged elastic moduli of the matrix constituent after matrix constituent failure occurs. Specifically, the value is the ratio of the failed matrix constituent moduli to the unfailed matrix constituent moduli. A value of 0.1 would mean that after a matrix failure occurs at an integration point, all six of the matrix constituent moduli (Em

11, Em22, E

m33, G

m12, G

m13, G

m23

) are reduced to 10% of the original undamaged matrix constituent moduli. The matrix post-failure stiffness value must be greater than 0, and less than or equal to 1. By default, the matrix post-failure stiffness value is set to 0.1. If the post-failure nonlinearity feature is turned on, this value will be ignored. For more information on the matrix post-failure stiffness, please refer to Appendix A.12 of this documentation.

For analyses using Energy-Based Degradation, this value is the total energy dissipated before and after a matrix failure assuming a linear degradation of composite stiffness after a failure event. Specifically, composite Ec

22, Ec33, G

c12, G

c13 and Gc

23

are degraded after a matrix failure event according to this energy, the composite stress state at fiber failure, and the volume of the element. For more information on the computation of the energy values, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual.

Note: For unidirectional materials, if the Post-Failure Nonlinearity feature is turned on, then the twelfth user material constant will be ignored since the matrix post-failure stiffness is determined by the Post-Failure Nonlinearity feature.

Note: For woven composites, if the matrix post-failure stiffness is specified, the third user

material constant (Progressive Failure analysis) must be set to a value of 2. If the third constant is set to a value of 1, the twelfth user constant will be ignored.

• Fiber Post-Failure Stiffness / Fiber Degradation Energy –For analyses not using Energy-

Based Degradation, the thirteenth user material constant is a fraction that is used to define the damaged elastic moduli of the fiber constituent after fiber constituent failure occurs. Specifically, the value is the ratio of the failed fiber constituent moduli to the unfailed fiber constituent moduli. A value of 0.01 would mean that after a fiber failure occurs at an integration point, all six of the fiber constituent moduli (Ef

11, Ef22, E

f33, G

f12, G

f13, G

f23

) are reduced to 1% of the original undamaged fiber constituent moduli. The fiber post-failure stiffness value must be greater than 0, and less than or equal to 1. The default value of the fiber post-failure stiffness is automatically set to 0.01. For more information on the fiber post-failure stiffness, please refer to Appendix A.12 of this documentation.

For analyses using Energy-Based Degradation, this value is the total energy dissipated for a fiber failure assuming a linear degradation of composite stiffness before and after a fiber failure event. Specifically, composite Ec

11, Gc12, and Gc

13

are degraded linearly after a fiber failure event according to this energy, the composite stress state at fiber failure, and the volume of the element. For more information on the computation of the energy values, refer to Appendix A.5 of this document and the Helius:MCT Theory Manual.

Note: For woven composites, if the fiber post-failure stiffness is specified, the third user material constant (Progressive Failure analysis) must be set to a value of 2. If the third constant is set to a value of 1, the thirteenth user constant will be ignored


Progressive failure analysis, pre-failure nonlinearity, post-failure nonlinearity, hydrostatic strengthening, post-failure stiffnesses and degradation energies do not

apply to Helius:MCT Linear

• User Material Constants 14, 15, 16 – .The 14th, 15th, and 16th user material constants are only required if the finite element model is defined using a custom system of units. If using a custom set of units, please refer to Appendix A.1 for formatting details.

4.2 Defining a Helius:MCT Cohesive Material A Helius:MCT cohesive material is defined similar to a composite material (Section 4.1) using the three keyword statements *MATERIAL, *DEPVAR, and *USER MATERIAL. Consider the following lines from an Abaqus input file that completely specify a Helius:MCT user-defined cohesive material. *MATERIAL, name=cohesive *DEPVAR 9 *USER MATERIAL, constants=11 23, 1.0E+10, 1.0E+10, 1.0E+10, 1.0E+6, 1.0E+6, 1.0E+6, 100 200, 200, 1.25 For any given Helius:MCT cohesive material, the number of user material constants must be between 8 and 11. Appendix B provides a detailed description of each of the user material constants, including the range of allowable values for each constant and the impact that each constant has on the constitutive relations used to represent the material. Each of the user material constants typically defined in an analysis incorporating a Helius:MCT cohesive material are listed below along with a brief description. For a more detailed description of any particular user material constant, refer to the appropriate section of Appendix B.

• Damage Criteria - The first user material constant selects the damage initiation and damage evolution criteria. It is a two digit integer where the tens place holds the damage initiation criterion selection and the ones place holds the damage evolution type selection. The damage initiation flag can be 1 for maximum traction or 2 for a quadratic based criterion. The damage evolution flag can be 1 for displacement based softening, 2 for energy based, or 3 for energy based using a mixed mode power law. For example, if the first user material constant is 12 the maximum traction damage initiation criterion will be used with the energy based softening law.

• Stiffnesses - User material constants 2-4 specify the material stiffness in the normal, first shear,

and second shear directions respectively.

• Strengths - User material constants 5-7 specify the maximum tractions the material can sustain before damage initiates in the normal, first shear, and second shear directions respectively.

• Displacement Based Damage Evolution - The following user material constants must be defined if the displacement based damage evolution is chosen.


o Effective Displacement at Failure - User material constant 8 is a positive number which defines difference in effective displacement at complete failure and at damage initiation.

• Energy Based Damage Evolution - The following user material constants must be defined if the energy based damage evolution is chosen. o Total Fracture Energy - User material constant 8 is a positive number which defines the

total energy dissipated due to a failure. In mathematical terms, this is the area under the traction - separation curve.

• Energy Based Damage Evolution (Mixed Mode Power Law) - The following user material constants must be defined if the energy based damage evolution with a mixed mode power law is chosen.

o Normal Mode Fracture Energy - User material constant 8 is a positive number which

defines the total energy dissipated due to a pure normal mode failure.

o First Shear Mode Fracture Energy - User material constant 9 is a positive number which defines the total energy dissipated due to a pure first shear mode failure.

o Second Shear Mode Fracture Energy - User material constant 10 is a positive number which defines the total energy dissipated due to a pure second shear mode failure.

o Power Law Exponent (Alpha) - User material constant 11 is a positive exponent used in the mixed mode power law function used to determine the rate of softening in the damaged cohesive material.

4.3 Modifying the Section Definitions After creating new material definitions for each of the Helius:MCT composite materials that appear in the Abaqus input file (described previously in Section 4.1), the next step is to incorporate the new materials into the various Section definitions that appear in the Abaqus input file. This process simply involves changing the name of each material ply in the composite section layup to the name of a valid Helius:MCT material that was defined as described in Section 4.1. For example, consider the following shell section definition excerpted from an Abaqus input file. *SHELL SECTION, elset=PlateLayup-1, composite, orientation=Ori1, stack direction=3, layup=PlateLayup 1., 3, MATERIAL_1, 0, Ply-1 1., 3, MATERIAL_1, 45, Ply-2 1., 3, MATERIAL_1, -45, Ply-3 1., 3, MATERIAL_1, 90, Ply-4 1., 3, MATERIAL_1, 90, Ply-5 1., 3, MATERIAL_1, -45, Ply-6 1., 3, MATERIAL_1, 45, Ply-7 1., 3, MATERIAL_1, 0, Ply-8 The composite section layup contains eight material plies, where each ply is composed of a material named "MATERIAL_1". This material name should be replaced by the name of the appropriate


Helius:MCT material, for example, "IM7_8552" as defined in Section 4.1. The updated shell section definition is shown below. *SHELL SECTION, elset=PlateLayup-1, composite, orientation=Ori1, stack direction=3, layup=PlateLayup, 1., 3, IM7_8552, 0, Ply-1 1., 3, IM7_8552, 45, Ply-2 1., 3, IM7_8552, -45, Ply-3 1., 3, IM7_8552, 90, Ply-4 1., 3, IM7_8552, 90, Ply-5 1., 3, IM7_8552, -45, Ply-6 1., 3, IM7_8552, 45, Ply-7 1., 3, IM7_8552, 0, Ply-8 Certain types of Abaqus elements (e.g., beam elements, shell elements, and reduced integration elements) require extraneous stiffness parameters in order to stabilize their response against deformation modes that are not governed directly by material constitutive relations. These extraneous stiffness parameters are defined as either options or data in the Section keyword statement that is referenced by the element in question. Depending upon the specific type of element being used, one or more of the following types of extraneous stiffness parameters may need to be specified as part of the Section definition that is referenced by the element.

• Section Poisson Ratio • Section Thickness Modulus • Section Transverse Shear Stiffnesses: Kts

11, Kts22, and Kts

12

• Membrane Hourglass Stiffness Control Parameter

• Bending Hourglass Stiffness Control Parameter

Appendix C.1 provides a detailed discussion of each type of extraneous stiffness parameter, in addition to listing the specific extraneous stiffness parameters that are required by each type of element. In earlier versions of Helius:MCT, the calculation of these extraneous stiffness parameters and their insertion in the Abaqus input file required a rather cumbersome manual procedure that is described in detail in Appendices C.2-C.4 of this User's Guide. However, Helius:MCT now includes an auxiliary program (xSTIFF) that automatically calculates and inserts the required extraneous stiffness parameters into the Abaqus input file. The use of xSTIFF is highly recommended as it greatly accelerates the model building process, while at the same time minimizing the chance for errors being introduced into the input file. With the availability of xSTIFF, the user can now postpone the task of defining the extraneous stiffness parameters until the model building process is completed and an Abaqus input file is saved. xSTIFF can then be run to automatically add any required extraneous stiffness parameters to the saved Abaqus input file. For more information on using xSTIFF to automatically calculate and insert the required extraneous stiffness parameters into the Abaqus input file, please refer to the xSTIFF User’s Guide. Note: If the user chooses to manually define the extraneous stiffness parameters, Appendices C.1-C.4

completely describe the processes of identifying the required extraneous stiffness parameters, calculating their values, and inserting the correctly formatted values into the Abaqus input file.


For cohesive sections, the response parameter must be set to RESPONSE = TRACTION SEPARATION.

4.4 Modeling Issues for Imposing Temperature Changes The composite materials that are stored in the Helius:MCT Composite Material Database are defaulted to have a stress-free temperature (cure temperature) of 0° in the system of units that is specified by the value of the 1st user material constant unless it is specified by the seventh user constant that the stress-free temperature stored in the material file should be used. Any initial temperature specified via the *INITIAL CONDITIONS, TYPE=TEMPERATURE statement (including the default value of 0°) will be used to calculate the residual stresses present in each of the constituents and the composite due to the unmatched coefficients of thermal expansion between the fiber and matrix. For details on how the temperature changes imposed in a model affect how Helius:MCT calculates residual stresses, please refer to Section 10 in the Helius Theory Manual.

4.5 Nonlinear Solution Control Parameters for Helius:MCT It is a widely accepted notion that good convergence (or any convergence at all) is difficult to achieve in a progressive failure simulation of a composite structure. In fact, many progressive failure simulations terminate early, not due to global structural failure, but simply due to the inability of the finite element code to obtain a converged solution at a particular load step. In light of this problem, one of the major advantages of Helius:MCT is that it has been optimized to significantly improve the overall convergence rate and robustness of finite element simulations of progressive failure of composite structures. However, in order to take full advantage of the superior convergence characteristics of Helius:MCT, the user must change some of the default settings that govern the nonlinear solution process used by Abaqus/Standard. These changes can be enacted using the *CONTROLS keyword statement. In Abaqus/Standard, the default settings for the nonlinear solution process are based on the fundamental assumption of the Newton-Raphson algorithm that the nonlinear response of the composite structure is sufficiently smooth at both the global and local levels. However, in a progressive failure simulation of a composite structure, the nonlinear response of the composite structure is not

smooth, especially at the local level where material failure results in an instantaneous reduction of material moduli. This non-smooth material response is one of the primary factors responsible for the difficulty in obtaining convergence in progressive failure simulations. Helius:MCT’s method of managing material nonlinearity is specifically designed to handle this localized non-smooth material response. However, the default settings of Abaqus’ convergence control parameters must be changed in order to allow Helius:MCT to improve the convergence characteristics of the finite element simulation. These default settings can be changed via the first data line of the *CONTROLS keyword statement. The *CONTROLS keyword statement should be placed in the input file immediately after the *STATIC keyword statement. The first data line in the *CONTROLS keyword statement contains 11 quantities. The default values of these 11 quantities are shown below in the *CONTROLS keyword statement below.

*CONTROLS, PARAMETERS=TIME INCREMENTATION 4,8,9,16,10,4,12,5,5,3,50 Qualitatively speaking, the changes that should be made to these default values are intended to significantly increase the number of equilibrium iterations that Abaqus/Standard will perform before the code evaluates the need for a reduction (or cut-back) in the time increment size. If Helius:MCT is used in


Nonlinear Solution Control Parameters are not used in Helius:MCT Linear.

the finite element solution, then the Abaqus input file should use the following *CONTROLS keyword statement. *CONTROLS, PARAMETERS=TIME INCREMENTATION 1000,1000,1000,1000,1000, , , , ,10,1000 Note that the value of the quantities 1, 2, 3, 4, 5 and 11 have been set to 1000, while the value of the 10th quantity has been set to 10. For all other quantities on the data line, the default values are acceptable. These changes force Abaqus to wait until 1000 equilibrium iterations have been completed before evaluating the need to reduce the time increment size. The familiar *STATIC keyword statement is present in the Abaqus input file for all quasi-static analyses. The single data line used by the *STATIC statement contains four quantities that collectively specify the desired time incrementation scheme. The first quantity specifies the size of the initial time increment. The second quantity specifies the total amount of time to be analyzed in the current step. The third quantity specifies the minimum allowable size of the time increments used in the current step. The fourth quantity specifies the maximum allowable size of the time increments used in the current step. Since the use of Helius:MCT significantly improves the ability of Abaqus to obtain a converged solution for any particular time increment, it is likely that the entire analysis can be performed without any time increment reductions; therefore, the user may wish to experiment with the parameters that he or she routinely employs in the data line of the *STATIC keyword statement.

4.6 Requesting Output of the MCT State Variables Solution-dependent MCT state variables are used to track the history of certain quantities that are computed in the Helius:MCT User-Defined Material Subroutine. Appendix D describes all 34 of the MCT state variables that pertain to unidirectional composites and all 90 of the MCT state variables that pertain to woven composites. These MCT state variables are not written to the output database file unless explicitly requested in the Abaqus input file. To request MCT state variable output, the user must add the identifying key ‘SDV’ to the list of output variables that are requested in the *ELEMENT OUTPUT keyword statement. For example, the following *ELEMENT OUTPUT keyword statement requests that stresses (S), strains (E), and MCT state variables (SDV) should be written in the output database file (note that the stresses (S) and strains (E) are not necessary for a Helius:MCT analysis but are included here for demonstrative purposes): *ELEMENT OUTPUT S,E,SDV

It should be emphasized that the number of MCT state variables that are written to the output file depends on the number of state varaibles that are requested by the *DEPVAR statement Another issue that should be considered when requesting output is the number and location of the section points where the output variables are calculated. In an element that contains multiple material layers, the default section points correspond to the top and bottom surface of the element, thus the output variables are not available for any of the internal material layers. If the user wishes to view the output variables for each of the material layers within an element, the user must explicitly list the section points


where the output variables should be computed. As an example, consider a 4 ply composite plate with 3 section points per ply, for a total of 12 section points as shown in Figure 9. By default, the output variables will only be computed for section points 1 and 12 corresponding to the top and bottom surfaces of the element. In order to view results for each material layer of the element, it is most expedient to request that the output variables should be computed at the mid-surface of each material layer (i.e., section points 2, 5, 8, 11). In order to request specific section points for the calculation of output variables, the user must add a data line immediately after the *ELEMENT OUTPUT keyword statement. This data line lists the specific section points where the output variables will be computed. For example, the following *ELEMENT OUTPUT keyword statement requests calculation of stress (S), strain (E) and the MCT state variables (SDV) at section points 2, 5, 8 and 11. *ELEMENT OUTPUT 2,5,8,11 S,E,SDV

Ply 1

Ply 2

Ply 3

Ply 4

X 1X 2X 3 X 4

X 5X 6 X 7

X 8X 9 X 10

X 11X 12

Figure 9: Location of section points within an element containing 4 material plies

Be aware that Abaqus allows only 16 quantities to be entered on the section point data line of the *ELEMENT OUTPUT keyword statement. For elements that contain large numbers of material layers, more than one *ELEMENT OUTPUT keyword statement is required to request all of the desired section points. For example, consider an element with 24 material layers. The following pair of *ELEMENT OUTPUT keyword statements is used to request output at the mid-surface of each of the 24 material layers. *ELEMENT OUTPUT 2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47 S,E,SDV *ELEMENT OUTPUT 50,53,56,59,62,65,68,71 S,E,SDV

4.7 Modeling Damage Tolerance in Composite Materials Damage tolerance is the ability of a structure to retain required structural strength or stiffness after it has sustained damaged. When a composite part is damaged, there are numerous failure modes that can exist. These failure modes are constituent-level defects (i.e. fiber and matrix level defects), so it is appropriate to model damage at this level. Helius:MCT is well-suited for modeling damage tolerance because it allows the user to specify constituent-level damage in elements at the start of the analysis. For


example, if a plate was impacted by a mass and there is diffuse matrix damage in impacted region, the user can create an element set that represents the damaged region and assign matrix failure to that region prior to the start of the analysis. At the start of the analysis, this region will have an SDV1 value of 2 (matrix failure) and as the simulation progresses, the region can undergo fiber failure which will result in an SDV1 value of 3. In other words, the initial value of SDV1 that is assigned to the element set is not fixed and can change if either the matrix or fiber failure criterion is satisfied. The initial value of SDV1 must be an integer value equal to 1, 2, or 3. For unidirectional materials, 1 corresponds to no failure, 2 corresponds to matrix failure, and 3 corresponds to fiber and matrix failure. For plain weaves, 1 corresponds to no failure, 2 corresponds to matrix failure in all tows and the matrix pocket, and 3 corresponds to fiber failure in all tows plus matrix failure in all tows and the matrix pocket. The Abaqus keyword, *INITIAL CONDITIONS, TYPE=SOLUTION is used to activate damage tolerance and is not supported by Abaqus/CAE. The following keyword statement demonstrates the use of damage tolerance with Helius:MCT. *INITIAL CONDITIONS, TYPE=SOLUTION DAMAGED_ELEMENTS, 3 In the above statement, DAMAGED_ELEMENTS is the name of the element set that represents the failed region and 3 indicates that this region will have fiber and matrix damage at the start of the analysis.


5 Running Helius:MCT on Linux

Before running Helius:MCT in a Linux environment it is assumed the following steps are done:

• The Abaqus input file has been created

• The utility provided by Firehole Composites to automatically write extraneous stiffness parameters to an Abaqus input file, xSTIFF, is not supported on Linux. Therefore, if the target input file uses any elements or sections that require extraneous stiffness parameters, xSTIFF must be executed on a supported Windows machine prior to copying the input file to the target Linux machine.

• The necessary Helius:MCT material files have been created and stored in the Firehole materials directory. Note the following.

o The application used to create Helius:MCT material files, Helius Material Manager, is not supported on Linux. Therefore, material files must be created on a supported Windows machine and copied to the target Linux machine.

o Helius:MCT resolves material files via the following convention:

MATERIAL_FILE_DIR/Material_Name/mdata.xml where Material_Name is the name of the name of the material in the Abaqus input file. Unlike Windows, Linux directories are case sensitive and Abaqus always modifies material names to use all upper-case characters. Therefore the Material_Name folder must always be in upper-case text.

• Abaqus has been pointed to the Helius:MCT libstandardU.so file. This is done via the usub_lib_dir variable in the abaqus_v6.env file. The variable must be set as one of the following (replace <FHTDIR> with the path of the base Firehole installation directory, i.e., /usr/local/firehole):

o usub_lib_dir = '<FHTDIR>/hmct/4.0' - For non cluster jobs o usub_lib_dir = '<FHTDIR>/hmct/4.0/mimd' - For jobs run on a cluster of

machines utilizing the Message Passing Interface (MPI).

This variable can be set in the global abaqus_v6.env file or if multiple users run jobs on this machine it is recommended to copy this file into the appropriate user's home directory. From there it can be modified. This file can also reside in the current working directory. Abaqus searches for this file in the following order:

o Current working directory o The user's home directory o The Abaqus site directory

See sections 3.1.1, and 3.2.2 of the Abaqus Analysis User's Manual for more information on the abaqus_v6.env file and the usub_lib_dir variable.

Once the above steps have been performed, the input file can be executed just as any other standard Abaqus analysis.


6 Examining Helius:MCT Results with Abaqus/Viewer

This section discusses the use of Abaqus/Viewer to examine the finite element results that are generated by Helius:MCT. It is assumed that the reader is familiar with using Abaqus/Viewer to view finite element results and perform any necessary post-processing of finite element results. Therefore, this section focuses on issues that are unique to the processes of examining and interpreting the progressive failure results generated by Helius:MCT. This section is divided into two parts, the first of which focuses on the generation of contour plots for the MCT state variables. The second part deals with the issue of correlating damage distribution with overall changes in structural stiffness, including the detection of global structural failure.

6.1 Using contour plots to view the MCT state variables The MCT state variables are element output variables stored at each integration point within each element. Consequently, the same familiar methods used to view the stress and strain fields at each time increment can be used to view the MCT state variables. However, in order to view any of the MCT state variables in Abaqus/Viewer, the Abaqus input file must first request that they be written to the Abaqus output database file (see Sections 3.5 and 4.5). For a complete description of each of the MCT state variables, refer to Appendix D. Contour plots are usually the most appropriate means of examining the distribution of the MCT state variables. To generate a contour plot within Abaqus/Viewer, click the contour icon or select Plot Contours On Deformed Shape from the main toolbar. The default variable Abaqus/Viewer plots is the von Mises stress. To view the MCT state variables that are computed by Helius:MCT, open the Field Output dialog box by selecting Result Field Output from the main toolbar. The MCT state variables (SDV1, SDV2, SDV3, …, etc.) are listed within the Field Output dialog box along with the more familiar variables such as stress (S) and strain (E). The number of SDVs that are available in the Field Output dialog box depends entirely on the number of SDVs that were requested by the Abaqus input file via the *DEPVAR keyword statement. Note that the SDV variables may have been renamed (SDV1 → MAT_STATE, SDV2 → FI_MATRIX, etc.) by the same *DEPVAR keyword statement. The fundamental MCT state variable is SDV1 which indicates the discrete damage state of the composite material. SDV1 is a real variable that can assume a finite number of discrete values between 1.0 ≤ SDV1 < 4.0. The specific set of discrete values that can be assumed by SDV1 depends upon the type of composite material (unidirectional or woven) and the specific set of material nonlinearity features that are used by Helius:MCT during the finite element solution (see Appendix D). As a specific example, if Helius:MCT is used on a unidirectional microstructure with its progressive failure feature activated and its pre-failure and post-failure nonlinearity features de-activated, then SDV1 can only assume the values 1.0, 2.0, or 3.0 as shown in the table below. However, regardless of the features requested, all the discrete values of SDV1 between 1 and 2 generally indicate some level of matrix failure, and all values between 2 and 3 generally indicate some form of fiber failure. An MCT file (*.mct) is generated when a Helius:MCT enhanced analysis is submitted and contains the specific set of values that can be assumed by SDV1 for each material in the model. It should be noted that contour plots of fully-integrated elements can show values of SDV1 that are less than 1 and greater than 4. This is entirely due to the scheme Abaqus uses to compute contour values. For element-based values, such as SDV1, the computations vary depending on several criteria. In general, the extrapolation of integration point values to the nodal locations is the reason SDV1 can be less than 1 and greater than 4 for fully-integrated elements. To view the exact values for SDV1 at each


integration point within a specific element, use the Probe Values tool in the Abaqus Query toolset. For more information on how contour values are computed, refer to Section 42.1.1 of the Abaqus/CAE v6.10 User’s Manual.

Unidirectional Microstructure Progressive Failure Analysis (activated) Pre-Failure Nonlinearity (de-activated) Post-Failure Nonlinearity (de-activated)

Allowable

Discrete Values for SDV1 Discrete Composite Damage State

1.0 No Failure or Degradation 2.0 Matrix Failure only 3.0 Matrix & Fiber Failure

Because SDV1 is a discrete real variable taking values 1.0 ≤ SDV1 < 4.0, it is important for the user to change the settings of Abaqus/Viewer so that a unique color contour is associated with each discrete value of integer value of SDV1. In the case where SDV1 can assume values of 1.0, 2.0, or 3.0, the user should set the number of color contours to 3. The number of contour intervals used in a contour plot can be specified from the Contour Plot Options dialog box, which is accessed by clicking Options Contour from the main toolbar. The Contour Plot Options dialog box is shown in Figure 10. Under the heading ‘Contour Intervals’, the user should choose ‘Discrete’ and then use the slider bar to select the number of discrete color contours to match the number of integer values that SDV1 can assume.

Figure 10: Contour Plot Options dialog box


Figure 11 shows two different 3-color contour plots of the integer variable SDV1 for an axially loaded composite plate with a central hole. In Figure 11, the use of three discrete colors makes it easy to identify the regions where each of the three discrete composite damage states occur. The blue elements (SDV1=1) are completely undamaged; the green elements (SDV1=2) have failed matrix constituents and undamaged fibers; the red elements (SDV1=3) have failed matrix constituents and failed fiber constituents. Note that the quilt contour plot shows the average value of SDV1 for each individual element, while the banded contour plot simply uses the values of SDV1 at the individual integration points to establish the color contours independent of the element boundaries.

Figure 11: Comparison of a banded contour plot and a quilt contour plot using three discrete color contours to represent distribution of SDV1=1,2,3

The remaining MCT state variables (SDV2, SDV3, SDV4, …,SDV90) are continuous real variables. Therefore, in generating contour plots of these variables, it is not critical to manage the number of color contours. Furthermore, the standard practices used in viewing stress and strain distributions are also appropriate for viewing SDV2, SDV3, SDV4, …, etc..


Selection of Section Points When viewing finite element solution results for laminated composite structures, the user must be acutely aware of the numbering of the section points through the thickness of multilayer elements. A contour plot will only use the values of the variable stored at a particular section point. Therefore, to view a contour plot for a specific material layer, the user must choose a section point that lies within that material layer. To choose a specific section point, access the Section Points dialog box by selecting Results Section Points from the main toolbar. The Section Points dialog box is shown in Figure 12. The default section point that is plotted by Abaqus/Viewer is the bottom section point (i.e., the section point at the bottom of the element). To view results for a particular material ply, the Plies option can be checked and the appropriate ply can be selected. To view results for all section points in the same plot, an envelope plot can be used by selecting the Envelope option. Envelope plots show the maximum absolute, maximum, or minimum value of the selected variable across all of the plies in a layup. For more information on selecting section points, refer to Section 40.4.8 of the Abaqus/CAE v6.10 User’s Manual.

Figure 12: Section Points dialog box As an example of the above recommendations, consider Figure 13 which shows envelope quilted contour plots of SDV1=1,2,3 at several points in time during a progressive failure analysis of a composite plate with a central hole. The plate has eight material plies and is loaded in tension. Since these contour plots are envelope plots, the color at any location represents the highest value of SDV1 that is achieved at any of the section points distributed through the thickness of the 8-ply laminate. In these plots, blue elements have no failure at any of the section points that are distributed through the laminate thickness. The green elements have at least one section point where matrix failure has occurred, while the red elements have at least one section point where both matrix failure and fiber failure occurred.


Figure 13: Envelope, quilted contour plots of SDV1 at several different points in time during a progressive failure analysis


Several important observations can be made regarding the sequence of envelope quilted contour plots shown in Figure 13:

• At time = 0.3, every element is blue, which means that no points in the composite plate have experienced any type of failure.

• At time = 0.4 there are some green elements at the edges of the hole. Within these green elements, at least one material ply has experienced a matrix constituent failure. However, the plot does not specify which of the material plies have experienced a matrix constituent failure.

• Comparing the plots at times 0.4 and 0.5 indicates the progression of matrix constituent failure as the load increases.

• At time = 0.7, the matrix failure has spread further, and there are three elements with fiber failure, as indicated by the red elements. Again, the red elements indicate that at least one of the 8 material plies has experienced a fiber constituent failure.

• At time = 0.9045, there is significant matrix failure, and the fiber failure has spread out towards the plate edges.

• At time = 1.0, there is additional matrix and fiber failure.

6.2 Detection of global structural failure In Section 6.1, we used color contour plots to examine the distribution of the discrete composite failure state (SDV1) within a composite structure. In viewing these contour plots, it is easily appreciated that each of the damaged regions represents material whose stiffness has been significantly degraded. Furthermore, by examining the changes that occur in these contour plots over time, we can clearly see the cascade of localized material failure that occurs during a progressive failure analysis. However, viewing the distribution of material failure does not

provide any indication of the overall impact of the material failure on the global stiffness of the structure. Moreover, it is impossible to detect global structural failure by simply examining the distribution of material failure over the structure.

In order to detect global structural failure or to associate a particular distribution of damage with a decrease in overall structural stiffness, we must first examine the relationship between global structural force and global structural deformation. This type of relationship is best examined using a simple 2-D plot of force vs. deformation; however, the key issue is to select an appropriate measure of global structural force and an appropriate measure of global structural deformation.

As an example, let us consider an 8-ply composite plate shown in Figure 14. Note that this is the same composite plate problem examined earlier in Section 6.1. As seen earlier in Figure 13, the distribution of damage within the composite plate is shown at several different points in time over the course of the analysis. However, simply viewing the contours plots shown in Figure 13 does not provide us with an understanding of how each of the damage distributions affects the global structural stiffness of the composite plate. To understand the degradation of global structural stiffness as localized failures spread throughout the composite plate, let us examine a simple 2-D plot of global structural force vs. global structural deformation. Since this composite plate is subjected to a uniform axial displacement that is imposed along the top edge of the plate, the imposed axial displacement will serve as an appropriate measure of the overall structural deformation in the plate. Similarly, the total axial reaction force along the top edge of the plate will serve as an appropriate measure of global structural force in the plate. This total reaction force is obtained by summing the nodal reaction forces for all of the nodes on the top edge of the plate (see Figure 15). Figure 16 shows a plot of global structural force vs. global structural deformation for the composite plate.


Figure 14: 8-ply composite plate under imposed axial displacement

Figure 15: The global structural force is obtained by summing the vertical reactions forces

at all nodes along the top edge of the composite plate


Figure 16: Global structural force vs. global structural deformation

Beginning at an imposed displacement of 0.13, the overall secant stiffness of the structure starts

to deteriorate rapidly. Beyond this point, as the imposed axial displacement is further increased, the structure is unable to resist the additional imposed displacement with additional structural force. Examination of Figure 16 reveals that the global force/displacement response of the composite structure appears to remain linear until the imposed displacement reaches a value of approximately 0.095. Interestingly, if we examine Part C of Figure 13, we see that by the time the imposed axial displacement has reached the value of 0.08, the composite plate has accumulated a significant amount of matrix constituent failure along the vertical edges of the circular hole. However, this amount of matrix constituent failure is insufficient to make a visually detectable impact on the global stiffness of the composite plate. As the imposed displacement is increased from 0.095 to approximately 0.13, the global stiffness of the composite plate undergoes a visually detectable reduction in Figure 16; however, the structure is still able to respond to increasing displacement with increasing structural force. In examining Part D of Figure 13, we see that at an imposed displacement of 0.112, the composite plate has experienced a small amount of fiber constituent failure along the vertical edges of the circular hole. Note that this localized fiber constituent failure has not yet prevented the composite plate from responding to increased displacement with increased structural force. As the imposed displacement reaches approximately 0.133, the global stiffness of the composite plate exhibits a drastic reduction indicting a significant cascading of localized fiber constituent failures (i.e., a major failure event has occurred). As the imposed displacement is increased beyond 0.133, the composite plate no longer responds to increasing


displacement with increasing structural force. Instead, the overall structural force in the composite plate remains relatively constant, indicating that the spread of localized failures is too rapid to build any additional structural force. However, as seen by the two dotted lines in Figure 16, the overall secant stiffness of the composite plate continues to decrease despite the fact that the overall structural force remains relatively constant. There are many possible ways to define global structural failure. The exact point that signals global structural failure depends upon the intended use of the composite plate. The point that should be emphasized here is that the detection of global structural failure requires an examination of the global structural force vs. global structural deformation. In summary, contour plots of the MCT state variables (especially SDV1) provide the analyst with a clear picture of the extent of localized failures at any particular point in time. In order to correlate any of the damage distributions with decreased overall stiffness of the composite structural, one must examine plots of global structural force vs. global structural deformation. In this way, the analyst can associate observed changes in the global stiffness of the structure with specific damage distributions.


Material constants 3-6 and 11-13 are not used in Helius:MCT Linear.

Appendix A User Material Constants for Composite Materials

A set of user material constants are provided in the data line that immediately follows the *USER MATERIAL keyword statement. The Helius:MCT User-Defined Material Subroutine uses these constants to determine the precise form of multiscale constitutive relations that should be used for the composite material. For any type of Helius:MCT composite material, the number of user material constants must be between 3 and 16. The first three user material constants are required for all Helius:MCT materials. The last three user material constants (i.e., the 14th, 15th, and 16th constants) are only required if the finite element model is defined using a custom system of units (see Appendix A.1). Table A1 provides a short description of the constitutive modeling issue that is controlled by each of the possible user material constants along with the allowable range of values for each constant.

Table A1. Helius:MCT User Material Constants For Composite Materials

User Material Constant

Constitutive Issue Controlled by the User Material Constant Allowable Values

1 System of Units 1,2,3,4,5

2 Principal Material Coordinate System Unidirectional → 1, 2 Woven → 1, 2, 3

3 Progressive Failure Analysis Uni → 0 (off), 1 (on) Woven → 0 (off), 1 or 2 (on)

4 Pre-Failure Nonlinearity 0 (off), 1 (on)

5 Post-Failure Nonlinearity / Energy-Based Degradation

0 (off) 1 (Post-Failure Nonlinearity)

2 (Energy-Based Degradation) 6 Hydrostatic Strengthening 0 (off), 1 (on)

7 Stress Free Temperature 0 (0°), 1 (temperature read from material file)

8 Not currently used 0 or blank 9 Not currently used 0 or blank 10 Not currently used 0 or blank 11 Average Element Thickness Must be greater than zero

12 Matrix Post Failure Stiffness / Matrix Degradation Energy

0 < value ≤ 1 / Must be greater than zero

13 Fiber Post Failure Stiffness / Fiber Degradation Energy

0 < value ≤ 1 / Must be greater than zero

14 Force Conversion for Custom Units Must be greater than zero 15 Length Conversion for Custom Units Must be greater than zero

16 Temperature Difference Conversion for Custom Units Must be greater than zero

In the remainder of Appendix A, each of the material constants is discussed in detail, including the impact of the constant on the multiscale constitutive relations used to represent the composite material.


Appendix A.1 User Material Constant #1: Systems of Units All numerical quantities in a finite element input file must be expressed in a consistent set of units. For example, if the geometry of the model is specified in centimeters and the force is specified in Newtons, then the material moduli must be expressed in units of N/cm2. All material properties in the Helius:MCT composite material database are stored using the (N/m/K) system of units (i.e., force is expressed in Newtons, length is expressed in meters, and temperature is expressed in degrees Kelvin). Therefore, if a model is built using a different system of units, then the user must identify the appropriate system of units so that Helius:MCT can provide stiffness and stress to the Abaqus/Standard finite element code in the correct units. Helius:MCT has pre-programmed conversion factors that can be used to express constitutive information in several commonly used systems of units. In addition, Helius:MCT has the capability to provide constitutive information in a user-defined (or custom) system of units. The system of units that will be used by the Helius:MCT User-Defined Material Subroutine is defined by the first user material constant listed on the data line that immediately follows the *USER MATERIAL statement. Table A2 shows the allowable range of integer values for the first user material constant and lists the system of units specified by each value.

Table A2. System of Units specified by User Material Constant #1

User Material Constant #1 System of Units

1 N, m, K 2 N, mm, K 3 lb, in, R 4 lb, ft, R 5 Custom

If the first user material constant is assigned a value of 1, 2, 3, or 4, then Helius:MCT will automatically perform the appropriate unit conversions and provide the constitutive relations in the system of units shown in Table A2. However, if the model is defined using a system of units that is not represented in Table A2, then the user must set the value of the first user material constant to 5, indicating that a 'custom' system of units will be used. In this case, the user must specify the three conversion factors that are needed by Helius:MCT to convert from the default units of Newtons, meters, and Kelvin to the custom system of units. These three conversion factors for force, length, and temperature will be listed as the 14th, 15th, and 16th user material constants respectively in the data line of the *USER MATERIAL statement. Note that the 14th, 15th, and 16th user material constants are required only if

the value of the 1st user material constant is 5.

As an example of a custom system of units, let’s say that a finite element model is created using units of kilonewtons, centimeters, and degrees Fahrenheit. Since this particular system of units is not included in Table A2, it will be considered a custom system of units. Consequently the first user material constant for any Helius:MCT materials should be assigned a value of 5. Now we must compute the conversion factors for force, length, and temperature that will be listed as the 14th, 15th, and 16th user material constants respectively. The force conversion factor that is required to convert from the default units of Newtons, to the desired units of kilonewtons is computed as,


NkN

NkNFconv 001.0

10001

== .

The length conversion factor that is required to convert from the default units of meters, to the desired units of centimeters is computed as,

mcm

mcmLconv 100

1100

== .

The conversion factor for temperature changes (∆T) that is required to convert temperature change from the default units of K to the desired units of °F is computed as,

∆KF

KFTconv

°=

°= 8.1

15/9 .

The 14th, 15th, and 16th user material constants should be assigned values of 0.001, 100, and 1.8 respectively. In this case, the data line immediately following the *USER MATERIAL statement would have sixteen user material constants as shown below. The first user material constant (value=5) indicates that a ‘custom’ system of units will be used. The 14th, 15th, and 16th user material constants specify the factors needed to convert from the default units of Newtons, meters, and Kelvin to the desired units of kilonewtons, centimeters, and degrees Fahrenheit respectively. An example of the *USER MATERIAL keyword statement is shown below. *USER MATERIAL, CONSTANTS=16 5, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0.1, 0.01, 0.001, 100, 1.8 Note that the *USER MATERIAL statement includes the parameter ‘CONSTANTS=16’ to indicate that there are sixteen user material constants on the data line. Two additional points should be emphasized regarding the choice of values for the 1st user material constant. First, all stress results printed in the Abaqus output files will be expressed in the units specified by the user via the first user material constant. For example, if the first user material constant has a value of 3 (specifying the pound, inch, degree Rankine system of units), Abaqus will output all stresses in units of lb/in2. Second, custom units are not supported by the Helius:MCT GUI and must be specified manually by the user by either changing the material definition in the Abaqus/CAE keyword editor or by directly editing the input (*.inp) file with a text editor such as Notepad.


Appendix A.2 User Material Constant #2: Principal Material Coordinate System

Helius:MCT expresses constitutive relations and computes stress in the principal material coordinate system of the composite material. For unidirectional microstructures, Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fiber direction, while the ‘2’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of Helius:MCT’s principal material coordinate system so that the ‘2’ direction is aligned with the fiber direction, while the ‘1’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy. For woven microstructures, Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fill tow direction, while the ‘2’ direction corresponds to the warp tow direction and the ‘3’ direction corresponds with the out-of-plane direction. However, in situations where it adds convenience or simplicity to the model creation process, the user may change the orientation of the principal material coordinate system so that the ‘2’ direction is aligned with the fill tow direction, while the ‘1’ direction corresponds to the warp tow direction. Additionally, the user may change the orientation of the principal material coordinate system so that the ‘3’ direction is aligned with the fill tow direction while the ‘2’ direction corresponds to the warp tow direction. The second user material constant is used to specify the orientation of the principal material coordinate system that will be used by Helius:MCT. The numerical value (1 or 2 for unidirectional materials and 1, 2 or 3 for woven materials) of the second user material constant specifies which of the principal material coordinate axes will be aligned with the fiber direction (for unidirectional composites) or the fill tow direction (for woven composites). The availability of alternative orientations for the principal material coordinate system provides the user with more flexibility in specifying the orientation of the material plies within a section definition. The user should be aware that Abaqus/Standard outputs the composite average state of stress and strain in the coordinate system that is specified by the second user material constant; however, the constituent average states of stress and strain (stored in SDV7, SDV8, ..., SDV90) are always output in Helius:MCT's default principal material coordinate system. As an example, if the second user material constant is specified as 2, all composite average stress and strain states will be output in the local system defined by the user, with the local 2 direction corresponding to either the longitudinal axis of the fibers for unidirectional materials, or the fill axis for woven materials. However, all constituent average stress and strain states will be reported in the default principal coordinate system of the unidirectional or woven composite material.

• For unidirectional microstructures, Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fiber direction, while the ‘2’ and ‘3’ directions lie in the composite material’s plane of transverse isotropy.

• For woven microstructures, Helius:MCT’s default principal material coordinate system is oriented with the ‘1’ direction aligned with the fill tow direction, while the ‘2’ direction corresponds to the warp tow direction and the ‘3’ direction corresponds with the out-of-plane direction.


Consider the following *USER MATERIAL statement that appears in an Abaqus input file representing a unidirectional microstructure. *USER MATERIAL, CONSTANTS=13 1, 2, 1, 0, 0, 0, 0, 0 0, 0, 0, 0.1, 0.01 Note that the second user material constant is assigned a value of 2. Therefore, this particular material will use a principal material coordinate system where the ‘2’ axis is aligned with the reinforcing fibers, and the ‘1’ and ‘3’ axes lie in the composite material’s plane of transverse isotropy. The following example problem illustrates the consequences of assigning the second user material constant a value of 2. Example: Consider a cylindrical tube that is composed of two unidirectional composite material plies (see Figure A17). Both composite plies are made of the same composite material, but the two plies differ in the orientation of the reinforcing fibers. The reinforcing fibers of the inner ply are aligned with the axial direction of the cylinder, and the reinforcing fibers of the outer ply are aligned with the hoop direction of the cylinder. The red lines in Figure A17 show the orientation of the reinforcing fibers in the inner and outer composite plies.

Figure A17. The fiber direction for each element is indicated by the red lines To illustrate the consequences of specifying a value of 2 for the second user material constant, consider the following statements that are excerpted from an Abaqus input file. The second user material constant is assigned a value of 2 indicating that the ‘2’ axis of the principal material coordinate system is aligned with the reinforcing fibers. Note that ** indicates a comment in an Abaqus input file. ** Define a Helius:MCT composite material. ** Note that the ‘2’ axis of the principal material ** coordinate system is aligned with the fiber direction. *MATERIAL, name=IM7_8552 *DEPVAR 6


*USER MATERIAL, CONSTANTS=13 1, 2, 1, 0, 0, 0, 0, 0 0, 0, 0, 0.1, 0.01 ** ** Define a local cylindrical coordinate system for the ** inner composite ply. Note that the local cylindrical ** coordinate system is rotated so that the local ‘2’ axis ** points in the global axial direction. *Orientation, name=axial_fibers, system=CYLINDRICAL 0., 0., 0., 0., 0., 1. 1, 90. ** ** Define a solid section for the inner composite ply. *Solid Section, elset=innerPly, orientation=axial_fibers, material=IM7_8552 ** ** Define a local cylindrical coordinate system for the ** outer composite ply. Note that there is no need to ** rotate the local cylindrical coordinate system since ** the local ‘2’ axis points in the global hoop direction. *Orientation, name=hoop_fibers, system=CYLINDRICAL 0., 0., 0., 0., 0., 1. 1, 0. ** ** Define a solid section for the outer composite ply. *Solid Section, elset=outerPly, orientation=hoop_fibers, material=IM7_8552 Notice that the orientation of the local cylindrical coordinate systems (given in the *ORIENTATION statements) must be consistent with the convention chosen for the principal material coordinate system. For example, the local cylindrical coordinate system for the inner ply is rotated so that the local ‘2’ axis points always points in the global axial direction. In contrast, the local cylindrical coordinate system for the outer ply does not need to be rotated since its local ‘2’ axis always points in the global hoop direction.


Progressive Failure Analysis is not available in Helius:MCT Linear.

Appendix A.3 User Material Constant #3: Progressive Failure Analysis The third user material constant is used to activate or deactivate Helius:MCT’s progressive failure analysis feature. If the progressive failure feature is activated, then Helius:MCT will routinely evaluate both the matrix failure criterion and the fiber failure criterion to determine if either constituent material has failed. Each constituent failure criterion is based on the corresponding constituent average stress state. For the purposes of this specific discussion, it is assumed that pre-failure and post-failure nonlinearity are de-activated. In the event that one or both of the constituents fail, the stiffness of the failed matrix and fiber are appropriately reduced to the values specified by the 12th and 13th material constants, respectively. Helius:MCT then calculates the current composite average stiffness based on the current state (failed, or not failed) of each constituent material. The value of the third user material constant has different implications depending on the microstructure of the material.

Unidirectional Microstructures: A value of 1 activates the progressive failure analysis feature, while a value of 0 deactivates the progressive failure analysis feature. Woven Microstructures: A value of 0 deactivates the progressive failure feature, a value of 1 activates the progressive failure feature and uses the matrix and fiber degradation levels from the material data file to calculate the failed material properties, and a value of 2 activates the progressive failure feature and uses the matrix and fiber degradations levels specified by the twelfth and thirteenth user material constants to calculate the failed material properties. Selecting a value of 2 for plain weaves will add approximately 45-60 seconds to the pre-processing time per woven material. A value of 1 will not add run-time during pre-processing because the failed material properties (at the matrix and fiber degradation levels specified during material creation in Helius Material Manager) are already stored in the material file.

The progressive failure analysis feature is the foundation component of Helius:MCT’s nonlinear multiscale constitutive relations. Other aspects of material nonlinearity can be invoked (via the 4th, 5th, and 6th user material constants); however, these additional forms of nonlinearity cannot be activated unless the progressive failure analysis feature is also activated. The discrete values that can be assumed by SDV1 differ depending on the microstructure of the underlying composite and additional forms of material nonlinearity invoked. A comprehensive listing of the allowable discrete values for SDV1 is provided in Appendix D. Additionally, a description of each discrete composite damage state is written in the summary file (*.mct) created by Helius:MCT during the preprocessing phase of the analysis. Figure A18 shows a [0°/ ±45°]s unidirectional composite plate that was analyzed using Helius:MCT’s progressive failure feature. Figure A18 shows a contour plot of the MCT state variable SDV1, representing the composite damage state in the 0° plies. The blue areas represent composite material with unfailed constituents (SDV1=1), the green areas represent composite material with a failed matrix constituent (SDV1=2), and the red areas represent composite material with matrix and fiber constituents that have failed (SDV1=3).


Figure A18: Helius:MCT solution for failure propagation in the 0° plies of a composite

laminate loaded in tension Note: The number of possible discrete damage states for the composite material depends on the type of composite material (unidirectional or woven) and the specific set of material nonlinearity features that are used by Helius:MCT. For any given case, a description of each discrete composite damage state and its associated SDV1 value is written in the summary file (*.mct) created by Helius:MCT during the preprocessing phase of the analysis. Additionally, the user is referred to Appendix C which describes all of the discrete damage states that can be assumed by any composite material under any circumstances. For further information on the Helius:MCT’s progressive failure analysis feature, refer to Section 4 of the Helius:MCT Theory Manual.

Failure Key No failure Matrix failure Matrix & Fiber Failure


Pre-Failure Nonlinearity is not available in Helius:MCT Linear.

Appendix A.4 User Material Constant #4: Pre-Failure Nonlinearity (Unidirectional composites only, not available for woven composites) The fourth user material constant activates or deactivates Helius:MCT’s pre-failure nonlinearity feature. A value of 1 activates the pre-failure nonlinearity feature, while the default value of 0 deactivates the pre-failure nonlinearity feature. The pre-failure nonlinearity feature is intended to account for the nonlinear longitudinal shear (softening) response that is commonly observed in fiber-reinforced composite materials prior to ultimate failure. This additional form of nonlinearity involves imposing a series of three discrete reductions in the longitudinal shear stiffness of the matrix constituent material (Gm

12 and Gm13) which directly results in a

corresponding series of three discrete reductions in the longitudinal shear stiffness of the composite material (Gc

12 and Gc13

Threshold

Interval 1 Interval 2 Interval 3

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80

10

20

30

40

50

60

70

80

Shear Strain (%)

Shea

r Stre

ss (M

Pa)

Experimental Data

Helius:MCT Pre Fail NL Off

Helius:MCT Pre Fail NL On

Threshold


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80

10

20

30

40

50

60

70

80

Shear Strain (%)

Shea

r Stre

ss (M

Pa)

Experimental Data



Threshold


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80

10

20

30

40

50

60

70

80

Shear Strain (%)

Shea

r Stre

ss (M

Pa)

Experimental Data



Com

posi

te A

vera

ge L

ongi

tudi

nal S

hear

Stre

ss (M

Pa)

Composite Average Longitudinal Shear Strain (%)

Longitudinal Shear Strength

measured data

progressive failure withoutpre-failure nonlinearity

progressive failure withpre-failure nonlinearity

matrix constituent failure

). Imposition of these three discrete reductions in the longitudinal shear moduli are completed prior to matrix constituent failure, thus providing a longitudinal shear softening effect prior to matrix failure. Figure A19 shows a typical measured longitudinal stress/strain curve for a unidirectional carbon/epoxy lamina. Helius:MCT’s pre-failure nonlinearity feature approximates this type of nonlinear longitudinal shear response with a four-segment, piecewise linear representation of the longitudinal shear response. For further information on the pre-failure nonlinearity feature, refer to Section 5 of the Helius:MCT Theory Manual. Appendix D details the discrete values that the solution state variable SDV1 can assume during a progressive failure analysis where the pre-fail nonlinearity feature is activated.

Figure A19: Comparison of predicted vs. measured longitudinal shear response for a typical fiber-reinforced composite lamina.


Post-Failure Nonlinearity and Energy-Based Degradation are not available in Helius:MCT Linear.

Appendix A.5 User Material Constant #5: Post-Failure Nonlinearity and Energy-Based Degradation

(Unidirectional composites only, not available for woven composites) The fifth user material constant activates or deactivates Helius:MCT’s post-failure nonlinearity or energy-based degradation features. A value of 1 activates the post-failure nonlinearity feature, a value of 2 activates the energy-based degradation functionality, while the default value of 0 deactivates the post-failure nonlinearity feature and the energy-based degradation feature.

Post-Failure Nonlinearity

Helius:MCT’s post-failure nonlinearity feature is intended to account for the residual load carrying capability of a failed composite lamina that is embedded in a composite laminate. If the post-failure nonlinearity feature is activated, then Helius:MCT will gradually reduce the stiffness of the matrix constituent material after the matrix failure criterion is triggered, instead of instantaneously reducing the matrix stiffness to its minimum value. In this case, the matrix failure criterion simply identifies the initiation of the matrix failure process (or the initiation of matrix cracking). After the matrix failure criterion is triggered, the matrix constituent stiffness is gradually reduced via a series four discrete stiffness reductions that are applied as the strain state continues to increase beyond the level present at matrix failure initiation. When using this feature, the MCT state variable SDV1 can be used to identify the condition of matrix crack saturation which is useful in determining leakage of a pressurized fluid through a composite laminate. For further information on the post-failure nonlinearity feature, refer to Section 6 of the Helius:MCT Theory Manual.


Figure A20: Helius:MCT stress-strain solutions for the central 90° ply within a (0/90/0)

laminate under axial tension, showing the effect of including the post-failure nonlinearity feature

Energy-Based Degradation

Helius:MCT’s energy-based degradation feature is intended to account for the residual load carrying capability of a failed composite lamina that is embedded in a composite laminate. If the energy-based degradation feature is activated, then Helius:MCT will gradually reduce the stiffness of the composite after a failure criteria is triggered, instead of instantaneously reducing the composite stiffness. In this case, the failure criterion simply identifies the initiation of failure. After the failure criterion is triggered, the composite constituent stiffness is gradually reduced via a series of discrete stiffness reductions that are applied as the strain state continues to increase beyond the level present at failure initiation. When using this feature, the MCT state variable SDV1 can be used to identify the progression of composite damage as the strain continues to increase. For a detailed description of the energy-based nonlinearity feature, refer to the Helius:MCT Theory Manual. The specific stiffness reductions that occur depend entirely on the failure state of the composite. Matrix Failures In the case of a matrix failure, composite Ec

22, Ec33, G

c12, G

c13, G

c23

degrade linearly using the relation

Pcd = (1.0 - dm) Pc

0

(A5)

where Pcd is the degraded composite property, Pc

0 is the virgin composite property, and dm

is the degradation constant due to matrix failure given by


dm = ε

feff(εeff - ε

0eff)

εeff(εfeff - ε

0eff)

. (A6)

In the above equation, εeff is a composite effective strain measure given by εeff = ε

222 + ε2

33 + ε212 + ε2

13 + ε223

, (A7)

ε

0eff is the value of the composite effective strain at matrix failure, and εf

eff

is the final effective strain value given by

εfeff =

2Gm

σ0effLe

, (A8)

where Gm is the total energy dissipated in the composite before and after a matrix failure (user material constants 12),

is the effective stress of the composite at matrix failure computed in the same manner as Equation A5, and Le is the representative element length defined by Abaqus. In the case of three-dimensional elements (i.e. bricks and continuum shell) the element length is the cubed root of the volume. In the case of two-dimensional elements (i.e. shell and plane stress elements) the element length is the square root of the area.

σ0eff

The definition of the final effective strain given in Equation A8 assumes a linear degradation of the effective stress vs. effective strain relationship of the composite, as shown in Figure A21.

Figure A21: Stress/strain response for a linear degradation using energy-based degradation.


To keep the MCT decomposition intact, and accurately capture the stresses in the constituents after a matrix failure, the properties of the matrix constituent are also degraded to enforce a consistent relationship from the micro to macro scale. Fiber Failures A fiber failure event will result in a linear degradation of composite Ec

11, Gc12, and Gc

13

in a similar manner to the degradation of the composite properties due to a matrix failure with the effective strain being defined as

εeff = ε211

, (A9)

and the effective stress defined in a similar manner. However, the longitudinal shear degradation is given by Pc

d = (1.0 - df) (1.0 - dm) Pc0

, (A10)

which forces the shear stiffness to be a strictly decreasing function of effective strain. The major difference between matrix failures and fiber failures is the need for constituent information. If the fiber fails, the matrix is assumed to fail as well, and the need for constituent information is not required for further failure calculations, so the constituent properties are not updated after fiber failures. Therefore, providing the dissipation energies for matrix and fiber failure events allows the energy-based degradation scheme to compute the degraded composite and constituent properties after a failure event as a function of increasing composite strain. The energy-based degradation will alleviate some mesh dependence on a final solution and provide a robust progressive failure analysis. Note: If the matrix constituent has failed prior to fiber failure Ec

22, Ec33, G

c23 are degraded according to the

Matrix Degradation Energy, otherwise Ec22, E

c33, G

c23

are degraded according to the Fiber Degradation Energy.

A Note on Discrete Interval Partitioning The Energy-Based damage feature of Helius:MCT uses multiple discrete intervals when linearly degrading the composite, as shown in Figure A22. Each interval uses a secant modulus to define the response of the composite in that specific interval. For problems where the total energy represents something similar to an isosceles triangle, the intervals will accurately capture the response of the composite.


Figure A22 Energy-based linear degradation interval partitioning.

For analyses where the total energy represents a very heavily skewed triangle, as shown in Figure A23, the interval partitioning will not accurately capture the linear softening of the composite at the early strain levels. This is entirely due to the number of intervals used to achieve the most rapid and robust convergence of the problem. Specifically, the stress secant intervals at strain levels near failure retain a high stiffness and can cause a misrepresentation of the stress state of the composite. If the user has analyses which must define a linear degradation curve in which the final effective strain is over 100 times the initial effective strain, please contact Firehole Composites for support.


Figure A23 Linear degradation for large energy problem using secant modulus interval divisions.


Hydrostatic Strengthening is not available in Helius:MCT Linear.

Appendix A.6 User Material Constant #6: Hydrostatic Strengthening (Unidirectional composites only, not available for woven composites) The sixth user material constant activates or deactivates Helius:MCT’s hydrostatic strengthening feature. A value of 1 activates the hydrostatic strengthening feature, while the default value of 0 deactivates the hydrostatic strengthening feature. If the hydrostatic strengthening feature is activated, then Helius:MCT explicitly accounts for the experimentally observed strengthening of the composite in the presence of a hydrostatic compressive stress in the matrix constituent. If the hydrostatic compressive stress in the matrix constituent exceeds a threshold value, then the strength of both the matrix constituent and the fiber constituent are scaled upwards commensurate with the level of hydrostatic compressive stress level in the matrix constituent. The threshold value of the matrix average hydrostatic compressive stress is an experimentally determined quantity denoted in index notation by σm*

kk , where σm*kk <0. Provided that the matrix average

hydrostatic compressive stress (σmkk = σm

11 + σm22 + σm

33) is negative and σmkk<σ

m*kk

, then the longitudinal shear strength of the matrix constituent is increased to,

Sm12 = Sm0

12 − 0.04(σmkk − σm*

kk )

, (A11)

where Sm12 is the new matrix average longitudinal shear strength and Sm0

12 is the original matrix average longitudinal shear strength. A hydrostatic strengthening ratio Sratio is computed as Sratio = (Sm

12)2/(Sm0

12 )2

. This ratio is then used to increase all of the coefficients of the matrix and fiber constituent failure criteria via

Ami = Am0

i ·Sratio

i=1,2,3,4,5, (A12a)

and Af

i = Af0i ·Sratio

i=1,2, (A12b)

where Am0i and Af0

i

denote the original strength coefficients that appear in the failure criteria for the matrix and fiber constituents, respectively.

For further information on the Helius:MCT’s hydrostatic strengthening feature, refer to Section 7 of the Helius:MCT Theory Manual.


Appendix A.7 User Material Constant #7: Thermal Residual Stresses (unidirectional composites only, not available for woven composites)

At room temperature, an unloaded laminated composite structure already has non-zero self equilibrating stresses at both the composite ply level and the constituent material level caused by the initial cooling of the structure from its elevated cure temperature to room temperature. At the composite ply level, these thermal residual stresses are caused entirely by differences in the thermal expansion characteristics of adjacent plies. At the constituent material level (fiber/matrix), the thermal residual stresses are caused in part by the previously mentioned ply level thermal residual stresses and in part by differences in the thermal expansion characteristics of the fiber and matrix materials. Helius:MCT can explicitly account for these ply-level and constituent-level thermal residual stresses that exist prior to any externally applied loads or temperature changes. In this case, the thermal residual stresses contribute to the total stress state of the composite material and thus influence the mechanical load level at which the material fails. The seventh user material constant (0 or 1) serves as a flag to turn this feature on or off.

If the seventh user material constant is specified as 1, then Helius:MCT computes the ply-level and constituent-level thermal residual stresses that are caused by the post-cure cool down from the stress-free temperature (i.e. cure temperature) to ambient temperature. In this case, the stress free temperature is read from the material data file (Mdata file) and ambient temperature corresponds to 72.5°F, 22.5°C or 295.65°K. If the seventh user material constant is specified as 1, ply-level and constituent-level thermal residual stresses will be present in the composite material prior to the application of any external mechanical and/or thermal loads that are imposed during the actual simulation. If the user chooses to explicitly account for thermal residual stresses in the analysis, then the user should verify the material data file (Mdata file) actually contains a defined stress free temperature; otherwise, the stress free temperature will default to 0° and the predicted thermal residual stresses will be quite erroneous.

If the seventh user material constant is specified as the default value of 0, then thermal residual stresses are not

[σ = C(ε−α∆T)] is simply computed as ∆T = T − Tsf = T. Several points should be emphasized here. First, the stress free temperature Tsf defaults to 0° even if the composite material data file (Mdata file) explicitly defines a non-zero stress free temperature. Second, regardless of the system of units that are employed by the finite element model, the current temperature T completely defines the temperature change ∆T that is used in the constitutive relations. Third, for composite materials that are characterized at multiple temperatures, the current temperature T will be used to interpolate the various material properties that contribute to the constitutive relations; consequently, it is recommended that a single-temperature characterization (i.e., a single-temperature Mdata file) should be used for the composite material in question. In summary, if the user does not request this option, then the current temperature T influences the constitutive relations in two different ways: 1) the temperature change used in the constitutive relations simply becomes ∆T=T, and 2) T is used to interpolate the temperature-dependent material properties that contribute to the constitutive relations.

included in the response of that particular composite material during the simulation. In this case, the stress free temperature of the composite material defaults to Tsf =0° (regardless of the system of units employed), and the temperature change that is used in the constitutive relations

It should be emphasized that the default temperature in Abaqus/Standard is 0°. This default temperature is completely compatible with the default stress free temperature of 0° that is assumed when the seventh user material constant is specified as 0. In this case, the model can still be subjected to


temperature changes by simply imposing a temperature other than 0°; however, these thermal stresses develop over the course of the analysis, as opposed to being present at the start of the analysis. For more information on thermal residual stresses, please refer to Section 10 of the Helius:MCT Theory Manual.


User Material Constant #11 is not available in Helius:MCT Linear.

Appendix A.8 User Material Constant #8: Not Currently Used Appendix A.9 User Material Constant #9: Not Currently Used

Appendix A.10 User Material Constant #10: Not Currently Used

Appendix A.11 User Material Constant #11: Average Element Thickness The eleventh user material constant is used to define the average element thickness used with energy-based degradation. For two-dimensional elements this value is ignored. For three-dimensional (solid) elements this is the average thickness the solid elements associated with the material, where the thickness is defined as the interlaminar dimension of the element. Recall from Appendix A.5 that the final effective strain used in the energy-based degradation calculations is given by

εfeff =

2Gm

σ0effLe

.

In the above, Le is the representative element length as defined by Abaqus (see Section 21.3.3 of the Abaqus Analysis User's Manual). In the case of three-dimensional elements (i.e. bricks and continuum shell) the element length is the cubed root of the volume. In the case of two-dimensional elements (i.e. shell and plane stress elements) the element length is the square root of the area. For two-dimensional elements, the element thickness is ignored, as the characteristic element length is giving a measure of the in-plane area of the element, carrying with it a meaningful measure to associate with a composite ply. However, for layered solid elements the representative element length is not associated with a measure for a single ply. To accommodate the use of solid elements and allow them to be used and compared against results for two-dimensional elements, the representative element length must be modified to provide a useful measure of the element length in the plane of a ply. Therefore, the average element thickness is used to compute a representative are for an element as follows:

Le = Ve

3

te

, (A13)

where Ve is the volume of the element, and te is the average thickness of the element. The element length defined in Equation A13 provides an accurate measure of the in-plane area of a solid element, and will collapse to the exact measure provided by Abaqus for two-dimensional elements when the thickness of a solid element is constant.


Appendix A.12 User Material Constant #12: Matrix Post-Failure Stiffness / Matrix Degradation Energy

The twelfth user material constant is used to define the response of the composite after a matrix failure. It can take the meaning of two different values depending on the requests of the user. Specifically, if the user requests energy-based degradation of the composite, this value represents the total energy dissipated by the composite before and after a matrix failure. Otherwise, this value is a fraction that is used to define the damaged elastic moduli of the matrix constituent after matrix constituent failure occurs. Matrix Post-Failure Stiffness Matrix post-failure stiffness is a fraction that is used to define the damaged elastic moduli of the matrix constituent after matrix constituent failure occurs. Specifically, the value is the ratio of the failed matrix constituent moduli to the unfailed matrix constituent moduli. As an example, for unidirectional and woven materials, a value of 0.10 would specify that after a matrix failure occurs at an integration point, all six of the matrix constituent moduli (Em

11, Em22, E

m33, G

m12, G

m13, G

m23

) are reduced to 10% of the original undamaged matrix constituent moduli. The matrix post-failure stiffness value must be greater than 0.0, and less than or equal to 1.0. In the event that the twelfth user material constant is not specified, the default value of 0.10 is assumed. Experimental data indicates that 10% is an acceptable value for matrix degradation in a multidirectional composite laminate comprised of unidirectional laminae; 70% is an acceptable degradation for laminates comprised of woven laminae.

Note: If the Post-Failure Nonlinearity feature is turned on, then the twelfth user material constant is ignored since the matrix post-failure stiffness is determined by the Post-Failure Nonlinearity feature.

Note: For woven composites, it is recommended that the matrix post-failure stiffness should not be less

than 0.7. Note: For woven composites, if the matrix post-failure stiffness is specified, the third user material

constant (Progressive Failure analysis) must be set to a value of 2. If the third constant is set to a value of 1, the twelfth user constant will be ignored.

The value of the twelfth user material constant can have a pronounced effect on the post-failure response of a multilayer composite structure since this constant is largely responsible for the rate at which local loads are redistributed after a localized matrix constituent failure occurs. Matrix Degradation Energy If the user requests energy-based degradation, this value represents the total energy of the composite before and after a matrix failure event. After a matrix failure event occurs, Ec

22, Ec33, G

c12, G

c13

, Gc23 are degraded linearly according to the linear degradation presented in Appendix A.5. As the

composite strain increases beyond initial matrix failure, the composite properties are reduced according to the input Matrix Degradation Energy, the composite strain at failure, the composite stress at failure, and the element volume. For more information on the Matrix Degradation Energy, refer to the Helius:MCT Theory Manual.


Note: After matrix failure, the matrix properties are calculated to enforce a correct MCT decomposition

when computing fiber failure indices for the remainder of the analysis. Note: If the Matrix Degradation Energy is specified as too low, the properties of the composite will be

instantaneously reduced (instead of gradually) to near zero when the matrix failure criterion exceeds 1.0. Refer to Appendix A.5 and the Helius:MCT Theory Manual for more information.



Appendix A.13 User Material Constant #13: Fiber Post-Failure Stiffness / Fiber Degradation Energy

The thirteenth user material constant is used to define the response of the composite after a fiber failure. It can take the meaning of two different values depending on the requests of the user. Specifically, if the user requests energy-based degradation of the composite, this value represents the total energy dissipated by the composite before and after a matrix failure. Otherwise, this value is a fraction that is used to define the damaged elastic moduli of the matrix constituent after matrix constituent failure occurs. Fiber Post-Failure Stiffness The fiber post-failure stiffness is a fraction that is used to define the damaged elastic moduli of the fiber constituent after fiber constituent failure occurs. Specifically, the value is the ratio of the failed fiber constituent moduli to the unfailed fiber constituent moduli. For unidirectional materials, a value of 0.01 would specify that after a fiber failure occurs at a particular integration point, all six of the fiber constituent moduli (Ef

11, Ef22, E

f33, G

f12, G

f13, G

f23) are reduced to 1% of the original undamaged fiber

constituent moduli at the integration point in question. For woven materials, a value of 0.01 would specify that after a fiber failure occurs at a particular integration point, three of the fiber constituent moduli (Ef

11, Gf12, G

f13

) are reduced to 1% of the original undamaged fiber constituent moduli at the integration point in question. The fiber post-failure stiffness value must be greater than 0, and less than or equal to 1. In the event that the thirteenth user material constant is not specified, the default value of 1E-06 is assumed.

Note: In response to a fiber constituent failure, the current implementation of Helius:MCT imposes an isotropic degradation of the fiber properties for unidirectional materials and an orthotropic degradation of the fiber properties for woven materials.

Note: For woven composites, if the fiber post-failure stiffness is specified, the third user material

constant (Progressive Failure analysis) must be set to a value of 2. If the third constant is set to a value of 1, the thirteenth user constant will be ignored.

The value of the thirteenth user material constant can have a pronounced effect on the predicted progressive failure response of a multilayer composite structure since this constant is largely responsible for the rate at which local loads are redistributed after a localized fiber constituent failure occurs. Consequently, as the value of the thirteenth user material constant is reduced from 1.0 toward 0.0, a local fiber failure is more likely to precipitate a cascade of localized fiber failures. Depending upon the magnitude of the fiber failure cascade, the result may be discernable as a noticeable softening of the overall structural response, or it may cascade without arresting and result in a global structural failure. Fiber Degradation Energy If the user requests energy-based degradation, this value represents the total energy of the composite before and after a fiber failure event. After a fiber failure event occurs, Ec

11, Gc12, and Gc

13 are degraded linearly according to Appendix A.5 for post-fiber failure. As the composite strain increases


beyond that at initial fiber failure, the composite properties are reduced according to the input Fiber Degradation Energy, the composite strain at failure, the composite stress at failure, and the element volume. For more information on the Fiber Degradation Energy, refer to the Helius:MCT Theory Manual. Note: After fiber failure, the matrix is assumed to have failed (whether it has or not), and the properties

of the constituents are no longer needed to compute failure. Therefore, the properties of the constituents are not updated after a fiber failure.

Note: If the matrix constituent has failed prior to fiber failure, Ec

22, Ec33, G

c23 are degraded according to

the Matrix Degradation Energy, otherwise Ec22, E

c33, G

c23

are degraded according to the Fiber Degradation Energy.

Note: If the Fiber Degradation Energy is specified as too low, the properties of the composite will be instantaneously reduced (instead of gradually) to near zero when the fiber failure criterion exceeds 1.0. Refer to Appendix A.5 and the Helius:MCT Theory Manual for more information.


Appendix B User Material Constants for Cohesive Materials

A set of user material constants are provided in the data line that immediately follows the *USER MATERIAL keyword statement. The Helius:MCT User-Defined Material Subroutine uses these constants to determine the precise form of multiscale constitutive relations that should be used for the cohesive material. For any type of Helius:MCT cohesive material, the number of user material constants must be between 8 and 11. Table B1 provides a short description of the constitutive modeling issue that is controlled by each of the possible user material constants along with the allowable range of values for each constant. Appendices B.1 - B.4 explain the user material constants in more detail. For a theoretical discussion of the cohesive material constitutive laws used in Helius:MCT please see the Helius:MCT Theory Manual.

Table B1: Helius:MCT User Material Constants for Cohesive Materials User

Material Constant

Constitutive Issue Controlled by the User Material Constant Allowable Values

1 Damage Criteria 11, 12, 13, 21, 22, 23 2 Normal Stiffness Knn > 0 3 First Shear Stiffness Kss > 0 4 Second Shear Stiffness Ktt > 0 5 Normal Maximum Traction Sn > 0 6 First Shear Maximum Traction Ss > 0 7 Second Shear Maximum Traction St > 0

8 Depends on damage evolution criterion. Please see Appendix B.4

δmf - δm

o > 0

GC > 12 teff

o δmo

GnC >

12 tn

o δno

9 First Shear Fracture Energy (used only for Mixed Mode, Power Law softening) Gt

C > 12 tt

o δto

10 Second Shear Fracture Energy (used only for Mixed Mode, Power Law softening) Gs

C > 12 ts

o δso

11 Exponent used in Mixed Mode, Power Law softening equation α > 0

Appendix B.1 User Material Constant #1: Damage Criteria The first user material constant specifies the damage criteria to use for the cohesive material. This constant must be a two digit integer. The tens place of the integer specifies the damage initiation criterion to use and can be a 1 or a 2. The ones place gives the damage evolution criterion and can be a 1, 2, or 3. Table B2 lists the valid values and which criteria they correspond to. See Appendices B.3-B.4 for descriptions of the damage criteria.


Table B2: Valid Values for User Material Constant 1 User Material

Constant 1 Damage Initiation Criterion Damage Evolution Criterion

11 Maximum Traction Displacement Based 12 Maximum Traction Energy Based 13 Maximum Traction Energy Based (Mixed Mode, Power Law) 21 Quadratic Traction Displacement Based 22 Quadratic Traction Energy Based 23 Quadratic Traction Energy Based (Mixed Mode, Power Law)

Appendix B.2 User Material Constants #2-4: Material Stiffness The stiffnesses of the cohesive material relate the separation of the cohesive layer to the tractions. The user must supply a valid stiffness for each direction of separation in the cohesive element. The three stiffness values are Knn, Kss, and Ktt which are the stiffnesses in the local three, one, and two directions respectively. A subscript of n denotes the local 3-direction, s denotes the local 1-direction, and t denotes the local 2-direction. The traction - separation relationship is given as:

tn

tstt

=

Knn 0 0

0 Kss 00 0 Ktt

εn

εsεt

where tn, ts, and tt are the tractions in the three directions. The nominal strains in the corresponding directions are εn, εs, and εt. The nominal strains are related to the three separations (δ) using the nominal thickness of the cohesive element, To.

εn

εsεt

=

δn / To

δs / Toδt / To

It is highly recommended to always use a nominal thickness of one. Note this value is explicitly defined in the cohesive section properties. It is not necessarily the physical thickness of the cohesive element. The response of the material is linear elastic until damage is initiated. Damage initiation is predicted differently depending on the criterion selected in user material constant one. See Appendix B.3 for more information on the available damage initiation criteria.

Appendix B.3 User Material Constants #5-7: Damage Initiation In order to predict damage initiation in a Helius:MCT cohesive material the user must supply valid "strength" properties of the material. These strengths are the maximum traction in each direction the material can sustain before damage initiates and stiffness of the material begins to reduce. The strengths in the local three, one, and two directions are provided via user material constants five, six, and seven, respectively. The criterion used to predict the point in the loading history where damage begins is selected using user material constant one (see Appendix B.1). The two options are Maximum Traction and Quadratic Traction.


Maximum Traction: The maximum traction criterion initiates damages when the following condition is met:

max

{ }tn

Sn,

tsSs

, ttSt

= 1

where Sn, Ss, and St are the maximum tractions in their respective directions the material can sustain before damage initiates. Quadratic Traction: The quadratic based criterion initiates damages when the following condition is met:

{ }tn

Sn

2

+

ts

Ss

2

+ tt

St

2

= 1

These criteria only predict when damage begins. They do not predict how damage evolves or how the material response changes after initiation. This is controlled by the damage evolution criterion selected. See Appendix B.4 for more information.

Appendix B.4 User Material Constants #8-11: Damage Evolution Once damage initiates in a cohesive material the stiffness of the material begins to reduce (damage evolves). Damage will continue to evolve as the deformation of the material continues to increase. Eventually the material will be considered fully damaged and contain zero stiffness. The reduced material stiffness is controlled by the damage variable, D, which is given as:

D = δm

f ( )δmmax - δm

o

δmmax( )δm

f - δmo

where δmo is the effective relative displacement at damage initiation, δm

max is the maximum effective relative displacement attained thus far in the loading history, and δm

f

is the effective relative displacement at complete failure. Effective displacement is defined as:

δm = { }δn

2 + δs2 + δt

2

where δn, δs, and δt are the three relative displacements in the local three, one, and two directions, respectively. The traction is then calculated using the original stiffness values and the damage variable as shown:

tn

tstt

=

( )1 - D Knn 0 0

0 ( )1 - D Kss 00 0 ( )1 - D Ktt

εn

εsεt

A typical traction displacement curve is shown in Figure B24. Damage initiates at δm

o where D = 0, and then damage continues to evolve to the point where D = 1 at δm

f .


Displacement

Trac

tion

δmo δ

mf

Figure B24. Typical cohesive material traction-displacement curve.

Displacement Based Damage Evolution: For the displacement based damage evolution criterion user material constant eight is interpreted as the difference between the effective relative displacement at complete failure, δm

f , and the effective relative displacement at damage initiation, δmo . Valid values must

be greater than zero. Figure B24 shows qualitatively how δmo and δm

f

relate to the rate of damage evolution.

Energy Based Damage Evolution: For the energy based damage evolution criterion user material constant eight is interpreted as the total fracture energy of the cohesive material, GC. Figure B25 shows how GC relates to the traction - separation response of the cohesive material. The value of GC supplied by the user is used to determine the final relative effective displacement as:

δmf =

2 GC

teffo

where teffo

is the effective traction at damage initiation.

Energy Based Damage Evolution (Mixed Mode, Power Law): The energy based mixed mode power law criterion uses fracture energies for each loading mode to determine damage evolution. Instead of a single fracture energy, GC, the user supplies the fracture energy for each mode (Gn

C , GsC , Gt

C

) via user material constants eight, nine, and ten respectively. The user must also supply an exponent, α, to be used in the power law. The power law states when the following condition is met the cohesive material has completely failed (D = 1):

Gn

GnC

α

+

Gs

GsC

α

+

Gt

GtC

α

= 1


where Gn, Gs, and Gt are the work done by the traction and the corresponding relative displacement in the local three, one, and two directions respectively.

Displacement

Trac

tion

GC

δmo δ

mf

Figure B25. Cohesive material response.


Appendix C Extraneous Stiffness Parameters

In order for Abaqus to be able to define the stiffness matrix for a particular element, Abaqus must be able to answer the following four questions:

1. Which materials reside within the element? 2. How is each material distributed within the element? 3. How is each material oriented within the element? 4. Beyond the basic stiffness that the element obtains directly from the constitutive relations of the

materials that are present within the element, are there any additional, extraneous stiffness parameters that are needed to improve, or stabilize the behavior of the element?

These four questions are answered within the Abaqus input file by a section definition, and

Abaqus/Standard requires that each element in a model must reference a section definition. Different types of section definitions (listed below) are referenced by different types of elements. * Membrane Section (referenced only by membrane elements) * Shell Section (referenced only by shell elements) * Shell General Section (referenced only by shell elements) * Solid Section (referenced only by 2-D and 3-D continuum elements) This appendix discusses the extraneous stiffness parameters mentioned in item 4 above. An understanding of these extraneous stiffness parameters becomes important when using materials that are defined in the Helius:MCT material database. In the event that a section definition includes only materials that are recognized Abaqus material types, Abaqus will automatically compute all of the extraneous stiffness parameters required in any given section definition. However, if a section definition uses one or more materials from the Helius:MCT material database, the user must compute the required extraneous stiffness parameters and list them as part of the section definition in the Abaqus input (*.inp) file. In response to this situation, the purpose of this appendix is threefold:

1. Identify the extraneous stiffness parameters that are required for each combination of element type and section definition type,

2. Define the format for listing the extraneous stiffness parameters in the section definition, and 3. Explain the manual method for calculating each of these extraneous stiffness parameters.

Note

: An auxiliary program (xSTIFF) is included with Helius:MCT. xSTIFF reads an Abaqus input file and automatically computes and inserts all of the extraneous stiffness parameters that are required by any reduced integration elements that utilize Helius:MCT composite materials. The availability of xSTIFF permits the user to forgo the time consuming and error prone manual process described in Appendices C.2 - C.4. The use of xSTIFF is highly recommended since it significantly reduces the model creation time while at the same time reducing the likelihood of errors being introduced into the Abaqus input file. For more information on the use of xSTIFF, please refer to the xSTIFF User’s Guide.

xSTIFF is only required for analyses that contain ply-based Helius:MCT materials. It is not required for analyses that use exclusively cohesive-based Helius:MCT materials.


Appendix C.1 Description of the Extraneous Stiffness Parameters There are four different types of extraneous stiffness parameters that might be required in a section definition depending upon the specific combination of section definition type and element type. These four extraneous stiffness parameters are listed below, along with a brief qualitative description of each. Hourglass Stiffness Control Parameters Certain types of elements that use reduced integration can exhibit spurious, so-called hourglass deformation modes without developing any internal stress in response to the deformation. The hourglass stiffness control parameters provide these elements with a suitable degree of resistance to the development of these spurious hourglass deformation modes without adversely affecting their resistance to realistic deformation modes. There are two commonly required types of hourglass stiffness control parameters: the membrane hourglass stiffness control parameter and the bending hourglass stiffness control parameter Section Transverse Shear Stiffnesses Kts

11, Kts22, and Kts

12 Abaqus shell elements do not derive their transverse shear stiffnesses directly from the constitutive relations of the materials that are present in the element. Instead, the transverse shear stiffnesses (

Kts11, K

ts22

, and Kts12

) of the element must be explicitly defined as part of the section definition that is referenced by the element.

Section Poisson Ratio The section Poisson ratio is used to define the thickness change of membrane elements and shell elements caused by the in-plane strains (i.e., membrane strains). Abaqus membrane and shell elements do not derive their section Poisson ratio directly from the constitutive relations of the materials that are present in the element. Instead, the section Poisson ratio of these elements must be explicitly defined as part of the corresponding section definition. Section Thickness Modulus

Abaqus continuum shell elements (SC6R and SC8R) explicitly account for an average transverse normal stiffness that controls thickness stretching and thickness contraction; consequently, these elements require a thickness modulus. However, Abaqus continuum shell elements do not derive their thickness modulus directly from the constitutive relations of the materials present in the element. Instead, the thickness modulus of the element must be explicitly defined as part of the shell section definition or the shell general section definition.

The following is a list of the extraneous stiffness parameters required for each different combination of section definition type and element type. *Membrane Section All membrane element types require the following parameter:

• Section Poisson Ratio Any membrane element that uses reduced integration requires the following parameter:

• Hourglass Stiffness Control Parameter


*Shell Section All shell element types require the following parameter:

• Section Poisson Ratio Any shell element that uses reduced integration requires the following parameters:

• Membrane Hourglass Stiffness Control Parameter • Bending Hourglass Stiffness Control Parameter

All shell elements that account for transverse shear stiffness (e.g., S3, S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, S8RT, SC6R, SC8R) require the following parameter:

• Section Transverse Shear Stiffnesses Kts11, K

ts22, and

All continuum shell elements require the following parameter: Kts

12

• Section Thickness Modulus *Shell General Section All shell element types require the following parameter:

• Section Poisson Ratio Any shell element that uses reduced integration requires the following parameters:

• Membrane Hourglass Stiffness Control Parameter • Bending Hourglass Stiffness Control Parameter

All shell elements that account for transverse shear stiffnesses (e.g., S3, S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, S8RT, SC6R, SC8R) require the following parameter:

• Section Transverse Shear Stiffnesses Kts11, K

ts22, and

All continuum shell elements require the following parameter: Kts

12

• Section Thickness Modulus *Solid Section Any continuum element that uses reduced integration requires the following parameter:

• Hourglass Stiffness Control Parameter


Appendix C.2 Formatting of the Extraneous Stiffness Parameters

Note: Appendix C.2 is intended only for those users that plan to manually compute the required

extraneous stiffness parameters and manually insert their formatted values into the Abaqus input file. Whenever possible, it is highly recommended to use the auxiliary program xSTIFF to perform this task automatically. For more information on the use of xSTIFF, please refer to the xSTIFF User’s Guide. Otherwise, Appendix C.2 defines the formatting requirements for the extraneous stiffness parameters for each type of section definition.

Membrane Sections A typical composite membrane section definition in the Abaqus input file has the following format: *Membrane Section, elset="elsetName", composite, orientation=orientationName 1., 3, materialName, 45., layer1 1., 3, materialName, 90., layer2 1., 3, materialName, 0., layer3 1., 3, materialName, -45., layer4 To add any or all of the required extraneous stiffness parameters to a Membrane Section definition, the following color-coded lines are added to the Membrane Section definition (in the positions shown below). *Membrane Section, elset="elsetName", composite, orientation=orientationName, POISSON=, … 1., 3, materialName, 45., layer1 1., 3, materialName, 90., layer2 1., 3, materialName, 0., layer3 1., 3, materialName, -45., layer4 *HOURGLASS STIFFNESS <HS data line> The single numerical quantity is the Section Poisson Ratio. The <HS data line> contains a single numerical quantity; interpreted as the Hourglass Stiffness Control Parameter (units are F/L2). Note: To calculate any of the numerical values required for , or <HS data line>, see “Calculation of Extraneous Stiffness Parameters,” in Appendix C.3.


Shell Sections A typical composite shell section definition in the Abaqus input file has the following format: *Shell Section, elset="elsetName", composite, orientation=orientationName 1., 3, materialName, 45., layer1 1., 3, materialName, 90., layer2 1., 3, materialName, 0., layer3 1., 3, materialName, -45., layer4 To add any or all of the required extraneous stiffness parameters to a Shell Section definition, the following color-coded lines can be added to the Shell Section definition (in the positions shown below). *Shell Section, elset="elsetName", composite, orientation=orientationName, POISSON=, THICKNESS MODULUS=<TM input value>, … 1., 3, materialName, 45., layer1 1., 3, materialName, 90., layer2 1., 3, materialName, 0., layer3 1., 3, materialName, -45., layer4 *HOURGLASS STIFFNESS <HS data line> *TRANSVERSE SHEAR STIFFNESS <TS data line> The single numerical quantity is the Section Poisson Ratio. The single numerical quantity <TM input value> is the Section Thickness Modulus. The <HS data line> contains four numeric quantities, described below. 1st Quantity: Membrane hourglass control parameter (units are F/L2). 2nd Quantity: Not used in shell elements 3rd Quantity: Bending hourglass control parameter (units are F/L2). 4th Quantity: Factor by which the default stiffness for rotation about the shell surface normal is to

be scaled (for shell nodes where six degrees of freedom are active). If this value is not entered or is entered as zero, Abaqus/Standard™ will use the default value.

The <TS data line> contains three numeric quantities, described below:

1st Quantity: Value of the transverse shear stiffness of the section in the first

direction, K11ts .

2nd Quantity: Value of the transverse shear stiffness of the section in the second

direction, K22ts .

3rd Quantity: Value of the coupling term in the shear stiffness of the section, K12

ts .


For Shell General Sections, the extraneous stiffness parameters receive the same formatting as shown above for Shell Sections. Note: To calculate any of the numerical values required for , <TM input value>, <HS data line>, or <TS data line>, see “Calculation of Extraneous Stiffness Parameters,” in Appendix C.3. Solid Sections A typical composite solid section definition in the input file (or Keywords Editor) has the following format: *Solid Section, elset="elsetName", composite, orientation=orientationName 1., 3, materialName, 45., layer1 1., 3, materialName, 90., layer2 1., 3, materialName, 0., layer3 1., 3, materialName, -45., layer4 To add the required hourglass stiffness control parameter to the Solid Section definition, the following lines shown in red font should be added to the end of the Solid Section definition: *Solid Section, elset="elsetName", composite, orientation=orientationName 1., 3, materialName, 45., layer1 1., 3, materialName, 90., layer2 1., 3, materialName, 0., layer3 1., 3, materialName, -45., layer4 *HOURGLASS STIFFNESS <HS data line> Note that <HS data line> contains two numerical quantities, described below. 1st Quantity: Hourglass control stiffness parameter (rFG) for use with solid elements. Units

are stress (F/L2). 2nd Quantity: Hourglass control stiffness parameter (rFK) is required only for the element type

C3D4H. Units of this parameter depend on the material property assigned to the element. For nearly incompressible elastomers (*HYPERELASTIC) and elastometric foams (*HYPERFOAM) the units are stress (F/L2 ); for all other remaining materials, including fully incompressible elastomers, the units are stress compliance (L2/F). If this value is left blank or entered as zero, Abaqus/Standard™ will use the default value.

Note: To calculate any of the numerical values required for <HS data line>, see “Calculation of Extraneous Stiffness Parameters,” in Appendix C.3.


Appendix C.3 Calculation of Extraneous Stiffness Parameters Note: Appendix C.3 is intended only for those users that plan to manually compute the required

extraneous stiffness parameters and manually insert their formatted values into the Abaqus input file. Whenever possible, it is highly recommended to use the auxiliary program xSTIFF to perform this task automatically. For more information on the use of xSTIFF, please refer to the xSTIFF User’s Guide. Otherwise, Appendix C.3 explains the semi-manual procedure for calculating the extraneous stiffness parameters that are required in an Abaqus input file.

As mentioned previously, Abaqus/Standard automatically calculates the values of all required extraneous stiffness parameters provided that the model only uses standard Abaqus material types. It is highly recommended that the user take advantage of this feature by running Abaqus in 'datacheck' mode and allowing it to automatically compute all of the extraneous stiffness parameters. However, before Abaqus can automatically compute the extraneous stiffness parameters, all of the model's user-defined material types must be converted to equivalent Abaqus/Standard material types. For the types of user-defined materials that can be accessed from the Helius:MCT material database, the most appropriate Abaqus/Standard material type is the elastic, orthotropic material type that is defined using the ‘*ELASTIC, TYPE=ENGINEERING CONSTANTS ' keyword statement..

This section explains how to execute Abaqus/Standard in datacheck mode to compute all of the extraneous stiffness parameters required in the various section definitions that appear in the Abaqus input file.

To run an Abaqus datacheck analysis, first make a copy of the existing Abaqus input (*.inp) file and rename it to distinguish it from the original copy. The datacheck analysis will be performed using the new copy of the input file; however, the new input file requires the following modification steps to enable Abaqus to compute the extraneous stiffness parameters and print the computed values in the *.dat file.

1. Insert the following *PREPRINT keyword statement at the beginning of the input file, just after the *HEADING keyword statement.

*PREPRINT, echo=no, MODEL=YES, history=no, contact=no

The parameter 'MODEL=YES' instructs Abaqus to print (in the *.dat file) all of the extraneous stiffness parameters that it calculates as part of the datacheck analysis.

2. Replace all existing *SHELL SECTION definitions with *SHELL GENERAL SECTION

definitions. Note that this step simply involves inserting the word ‘GENERAL’ into the appropriate section definitions; it does not involve changing any of the data of these section definitions.


3. Locate all of the Helius:MCT material definitions in the input file. Each of these Helius:MCT material definitions is composed of several different keyword statements. A typical material definition for a Helius:MCT material is shown below.

*Material, name=IM7_8552 *User Material, constants=13 1., 1., 1., 0., 0., 0., 0., 0. 0., 0., 0., 0.1, 0.01 *Depvar 6,

Each Helius:MCT material definition must be replaced with a recognized Abaqus material definition, specifically, an elastic, orthotropic material definition that has the same name as the original Helius:MCT material definition. The new elastic, orthotropic material definition is shown below.

*Material, name=IM7_8552 *Elastic, type=ENGINEERING CONSTANTS E11, E22, E33, v12, v13, v23, G12, G13 G23

The orthotropic elastic constants (E11, E22, E33, v12, v13, v23, G12, G13, G23) can be obtained by using the Helius:MCT GUI to access the Helius:MCT material database. For the specific case of the material IM7_8552, the Helius:MCT GUI displays the view shown in Figure C26. The engineering constants shown in Figure C26 can now be inserted into the new orthotropic elastic material definition as shown below.

*Material, name=IM7_8552 *Elastic, type=ENGINEERING CONSTANTS 2.03e+07, 1.65e+06, 1.65e+06, 0.324, 0.324, 0.461, 6.89e+05, 6.89e+05 5.65e+05


Figure C26: Helius:MCT GUI with IM7_8552 selected as a material


4. The datacheck analysis is now ready to be run. To run the datacheck analysis, the Abaqus Command window needs to be opened (

5. Figure C27).

Figure C27: Abaqus Command window from which to run the datacheck analysis

6. The following commands need to be entered into this window ( 7. Figure C28):

a. >>cd <directory in which .inp file is located>

Example: >>cd C:\Abaqus

b. >>abaqus datacheck job=<name of .inp file without the .inp extension> Example: >>abaqus datacheck job=example


Figure C28: Sequence of commands to run a datacheck analysis


8. After the final line of the command window is entered, a datacheck analysis will run in the same directory as the input file location. The extraneous stiffness parameters that are computed by Abaqus are printed in the *.dat file. When the analysis is complete, open the *.dat file using a text editor (e.g., Notepad, Wordpad, etc.).

9. The user will need to determine which type of section (shell, solid, membrane, or any

combination) contains Helius:MCT user materials. The following step will differ based on if the model contains solid, shell, or membrane sections. Step 8 in this User’s Guide is for a model containing only solid and shell sections. Similar procedures are executed for models containing membrane sections.

10. For a model containing solid sections, the *HOURGLASS STIFFNESS parameters for each solid section are located under the heading “S O L I D S E C T I O N (S)” in the *.dat file. Each section has a separate Property Number associated with it (see below). The ordering of the Property Numbers is based on the ordering of the instance keywords at the assembly level within the *.inp file. Each part keyword has a finite number of section keywords assigned to that part. Each part has a corresponding instance. The ordering scheme is then how the individual section keywords would appear if the parts were ordered in the same order that the instances appear. The *HOURGLASS STIFFNESS values are located near the bottom of the property number “HOURGLASS CONTROL STIFFNESS” (see below). PROPERTY NUMBER 1 SECTION ORIENTATION NAME ASSEMBLY_PLATE-1_ORI-1 NUMBER OF LAYERS 4 STACK DIRECTION 3 NUMBER OF INTEGRATION POINTS 4 LAYER 1 RELATIVE THICKNESS 0.2500 POINTS 1 MATERIAL IM7/8552 ORIENTATION LAYER 2 RELATIVE THICKNESS 0.2500 POINTS 1 MATERIAL IM7/8552 ORIENTATION ANGLE 45.00 DEGREES LAYER 3 RELATIVE THICKNESS 0.2500 POINTS 1 MATERIAL IM7/8552 ORIENTATION ANGLE -45.00 DEGREES LAYER 4 RELATIVE THICKNESS 0.2500 POINTS 1 MATERIAL IM7/8552 ORIENTATION ANGLE 90.00 DEGREES THE ROTATION ANGLES ARE MEASURED RELATIVE TO THE LOCAL 3 DIRECTION OF THE SECTION ORIENTATION HOURGLASS CONTROL STIFFNESS 2963.3

The hourglass control stiffness value ( 2963.3) should be added to the corresponding solid section definition in the original *.inp file, as shown below.


** Section: sectionName *Solid Section, elset="elsetName", composite, orientation=orientationName 1., 3, materialName, 45., layer1 1., 3, materialName, 90., layer2 1., 3, materialName, 0., layer3 1., 3, materialName, -45., layer4 *HOURGLASS STIFFNESS 2963.3

For a model containing membrane and/or shell section definitions, the extraneous stiffness parameters that are computed by Abaqus can include any or all of the following: hourglass stiffness control parameters, transverse shear stiffnesses, section Poisson ratio, and/or thickness modulus. These parameters can be found in the *.dat file under the general headings of “M E M B R A N E S E C T I O N (S)” and/or “S H E L L S E C T I O N (S)”. Within each of these general headings, each section definition is assigned a separate property number. The ordering of the Property Numbers is based on the ordering of the instance keywords at the assembly level within the *.inp file. Each part keyword has a finite number of section keywords assigned to that part. Each part has a corresponding instance. The ordering scheme is then how the individual section keywords would appear if the parts were ordered in the same order that the instances appear. For illustration purposes, a portion of the *.dat file, excerpted from general heading “S H E L L S E C T I O N (S)” is shown below. This portion lists the parameters specifically computed for the second shell section definition that appeared in the *.inp file (hence the label "PROPERTY NUMBER 2"). The excerpted text has been color coded to aid in locating the various extraneous stiffness parameters (section Poisson ratio, hourglass stiffness control parameters, transverse shear stiffnesses, section thickness modulus).

PROPERTY NUMBER 2 ADDED MASS PER UNIT AREA IS 0.0000 SECTION POISSON RATIO (USED WITH CONVENTIONAL FINTE STRAIN SHELLS ONLY) = 0.50000 EFFECTIVE THICKNESS ELASTICITY (USED WITH SC6R(T) AND SC8R(T) ELEMENTS ONLY) D3333 D3311 D3322 1.38200E+06 1.0000 1.0000

THE MIDDLE SURFACE OF THE SHELL IS THE REFERENCE SURFACE (NOT APPLICABLE FOR SC6R(T) AND SC8R(T) ELEMENTS)

GENERAL SECTION COMPOSITE WITH 4 LAYERS SECTION STIFFNESS MATRIX 3.51261E+07 1.12994E+07 4.12604E-10-2.82143E+07-1.16415E-10-4.70238E+06 1.12994E+07 3.51261E+07 2.99750E-08-1.16415E-10 2.82143E+07-4.70238E+06 4.12604E-10 2.99750E-08 1.19134E+07-4.70238E+06-4.70238E+06 0.0000 -2.82143E+07-1.16415E-10-4.70238E+06 5.59842E+07 5.91649E+06 9.62744E-10


-1.16415E-10 2.82143E+07-4.70238E+06 5.91649E+06 5.59842E+07 6.99416E-08 -4.70238E+06-4.70238E+06 0.0000 9.62744E-10 6.99416E-08 6.73512E+06

GENERALIZED STRESSES CAUSED BY THERMAL STRAINS 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 SCALING FACTORS SECTION THERMAL TEMPERATURE STIFFNESS EXPANSION 1.0000 1.0000 ORIENTATION ASSEMBLY_PLATE-1_ORI-3

TRANSVERSE SHEAR STIFFNESSES FOR THE SECTION Kts11 Kts22 Kts12 9.49571E+05 9.49571E+05 5.40040E-12 HOURGLASS CONTROL STIFFNESS

HOURGLASS CONTROL STIFFNESS (USED WITH S4R(T), S4R5, S9R5, S8R5, AND SC8R(T) ELEMENTS ONLY) MEMBRANE BENDING 3455.0 2591.2

After locating the values of the required extraneous stiffness parameters, the shell section definition can be modified as shown below.

** Section: sectionName *Shell Section, elset="elsetName", composite, orientation=orientationName, THICKNESS MODULUS=1.38200E+06, POISSON=0.50000, … 1., 3, materialName, 45., layer1 1., 3, materialName, 90., layer2 1., 3, materialName, 0., layer3 1., 3, materialName, -45., layer4 *HOURGLASS STIFFNESS 3455.0, ,2591.2 *TRANSVERSE SHEAR STIFFNESS 9.49571E+05, 9.49571E+05, 5.40040E-12

11. A Helius:MCT failure analysis can now be executed.


Appendix C.4 Using Abaqus/CAE to insert the Extraneous Stiffness Parameters

Note: Appendix C.4 is intended only for those users that plan to manually compute the required

extraneous stiffness parameters and manually insert their formatted values into the Abaqus input file. Whenever possible, it is highly recommended to use the auxiliary program xSTIFF to perform this task automatically. For more information on the use of xSTIFF, please refer to the xSTIFF User’s Guide. Otherwise, Appendix C.4 explains the use of Abaqus/CAE in manually entering the values of the extraneous stiffness parameters into an Abaqus input file.

After using the procedure described in Appendix C.3 to compute the values of the required extraneous stiffness parameters, there are two options for inserting the values into the Abaqus input file. First, the user can directly insert the values into the Abaqus input file using a text editor. In this case, the user must be aware of the formatting requirements for entering the extraneous stiffness parameters into the various Section definitions (see Appendices C.2 and C.3 for formatting requirements). A second option is to import the Abaqus input file back into Abaqus/CAE and use the various editing windows to enter the extraneous stiffness parameters. The remainder of this section explains the procedure for using Abaqus/CAE for entering the extraneous stiffness parameters. After importing the Abaqus input file back into Abaqus/CAE, the user can specify the values of the Section Poisson Ratio, Section Thickness Modulus, and Section Transverse Shear Stiffnesses in the Composite Layup Editor (see Figure C29). To access the Composite Layup Editor from the Property module, click Composite Edit “name of layup” from the main toolbar. In Figure C29, the appropriate entry boxes are highlighted. Note that these values can also be specified using a composite section, as opposed to the composite layup editor.

Figure C29: Locations of Section Poisson’s Ratio, Thickness Modulus, and Transverse Shear Stiffness settings in the Edit Composite Layup dialog box


The user can specify the values of the Membrane Hourglass Stiffness Control Parameter and Bending Hourglass Stiffness Control Parameter in the Element Type dialog box, which is accessed from the Mesh module by clicking Mesh Element Type from the main toolbar. Figure C30 shows the Element Type dialog box for a conventional shell element (S4R) with the hourglass stiffness entry boxes highlighted.

Figure C30: Locations of hourglass stiffness settings in the element type dialog box For continuum shell elements (SC6R or SC8R elements), there is a known bug in versions 6.8 and 6.9 of Abaqus/CAE that affects the Element Type dialog box. The Element Type dialog box only permits the user to enter the membrane hourglass stiffness parameter; no space is provided to specify the bending hourglass stiffness parameter. In light of these Abaqus/CAE bugs, the hourglass stiffness parameters for continuum shell elements can be entered via the Abaqus/CAE keywords editor or manually entered in the Abaqus input file using a text editor (discussed in Section 4). The bending hourglass stiffness parameter can be entered using the Keywords Editor after the membrane hourglass stiffness parameter has been defined through the Element Type dialog box. To access the Keywords Editor, click on Model Edit Keywords “Name of Model” from the main toolbar. Figure C31 shows an example of the Keyword Editor for a continuum shell section. Note the data line (2500., , 0., 0.) that immediately follows the *Hourglass Stiffness command. The third value in this data line specifies the bending hourglass stiffness parameter. As an example, let us assume the value of the bending hourglass stiffness parameter for this


particular section is 1700. The third value, currently 0, should be manually changed from 0 to 1700. The *Hourglass Stiffness command should now appear as:

*Hourglass Stiffness 2500., , 1700., 0.

Figure C31: Location of hourglass stiffness parameters in the keywords editor


SDV1 is not utilized in Helius:MCT Linear.

Appendix D MCT State Variables for Composite Materials

This appendix provides a description of all solution-dependent MCT state variables. There are a total of 34 MCT state variables for unidirectional composites and 90 MCT state variables for woven composites. These solution-dependent state variables are computed or updated by the Helius:MCT User-Defined Material Subroutine at each integration point within each finite element. Abaqus/Standard stores the converged values of solution-dependent MCT state variables for each time increment. Unless the MCT state variables are explicitly renamed via the *DEPVAR statement in the Abaqus input file, the Abaqus/Standard default naming convention for the MCT solution-dependent state variables is SDVi, where i=1,2,3,…,# of state variables. This appendix provides a complete description of all MCT state variables. For both unidirectional composites and woven composites, the first state variable (SDV1) has the same interpretation; however, the interpretation of the remaining state variables (SDV2, SDV3, ...) depends on the type of composite material (unidirectional or woven). The following list describes each of the MCT state variables (SDV1, SDV2, SDV3, ...) for unidirectional and woven composite materials. SDV1: SDV1 (often renamed as MAT_STATE) is a real variable that represents the discrete damage

state of the composite material by assuming a finite number of discrete values between 1 and 3. The number of discrete values that can be assumed by SDV1 and the interpretation of those discrete values depend upon the type of composite material (i.e. unidirectional or woven) and the specific set of material nonlinearity features that are employed by Helius:MCT to describe the materials response. The following five tables provide the interpretation for each allowable discrete value of SDV1 for each possible combination of composite material type and set of material nonlinearity features.

Unidirectional Composite Material Progressive Failure Analysis (activated) Pre-Failure Nonlinearity (de-activated) Post-Failure Nonlinearity (de-activated)

Energy-Based Degradation (de-activated) Allowable


1.0 Undamaged Matrix, Undamaged Fiber 2.0 Failed Matrix, Undamaged Fiber 3.0 Failed Matrix, Failed Fiber


Unidirectional Composite Material Progressive Failure Analysis (activated)

Pre-Failure Nonlinearity (activated) Post-Failure Nonlinearity (de-activated)



1.0 Undamaged Matrix, Undamaged Fiber 1.25 Matrix Pre-Failure Degradation Level 1, Undamaged Fiber 1.5 Matrix Pre-Failure Degradation Level 2, Undamaged Fiber 1.75 Matrix Pre-Failure Degradation Level 3, Undamaged Fiber 2.0 Failed Matrix, Undamaged Fiber 3.0 Failed Matrix, Failed Fiber

Unidirectional Composite Material Progressive Failure Analysis (activated) Pre-Failure Nonlinearity (de-activated) Post-Failure Nonlinearity (activated)



1.0 Undamaged Matrix, Undamaged Fiber 2.0 Matrix Post-Failure Degradation Level 1, Undamaged Fiber 2.25 Matrix Post-Failure Degradation Level 2, Undamaged Fiber 2.5 Matrix Post-Failure Degradation Level 3, Undamaged Fiber 2.75 Failed Matrix (Crack Saturation), Undamaged Fiber 3.0 Failed Matrix (Crack Saturation), Failed Fiber


Unidirectional Composite Material Progressive Failure Analysis (activated) Pre-Failure Nonlinearity (de-activated) Post-Failure Nonlinearity (de-activated) Energy-Based Degradation (activated)

Allowable Discrete Values

for SDV1 Discrete Composite Damage State 1.0 Undamaged Matrix, Undamaged Fiber 2.0 Matrix Post-Failure Degradation Level 1, Undamaged Fiber 2.038 Matrix Post-Failure Degradation Level 2, Undamaged Fiber ⋮

2.923 Matrix Post-Failure Degradation Level 25, Undamaged Fiber 2.962 Failed Matrix (Crack Saturation), Undamaged Fiber 3.0 Fiber Post-Failure Degradation Level 1 3.038 Fiber Matrix Post-Failure Degradation Level 2 ⋮

3.923 Fiber Post-Failure Degradation Level 25 3.962 Complete Fiber Failure


Pre-Failure Nonlinearity (activated) Post-Failure Nonlinearity (activated)



1.0 Undamaged Matrix, Undamaged Fiber 1.25 Matrix Pre-Failure Degradation Level 1, Undamaged Fiber 1.5 Matrix Pre-Failure Degradation Level 2, Undamaged Fiber 1.75 Matrix Pre-Failure Degradation Level 3, Undamaged Fiber 2.0 Matrix Post-Failure Degradation Level 1, Undamaged Fiber 2.25 Matrix Post-Failure Degradation Level 2, Undamaged Fiber 2.5 Matrix Post-Failure Degradation Level 3, Undamaged Fiber 2.75 Failed Matrix (Crack Saturation), Undamaged Fiber 3.0 Failed Matrix (Crack Saturation), Failed Fiber



Pre-Failure Nonlinearity (activated) Post-Failure Nonlinearity (de-activated) Energy-Based Degradation (activated)

Allowable Discrete Values

for SDV1 Discrete Composite Damage State 1.0 Undamaged Matrix, Undamaged Fiber 1.25 Matrix Pre-Failure Degradation Level 1, Undamaged Fiber 1.5 Matrix Pre-Failure Degradation Level 2, Undamaged Fiber 1.75 Matrix Pre-Failure Degradation Level 3, Undamaged Fiber 2.0 Matrix Post-Failure Degradation Level 1, Undamaged Fiber 2.038 Matrix Post-Failure Degradation Level 2, Undamaged Fiber ⋮

2.923 Matrix Post-Failure Degradation Level 25, Undamaged Fiber 2.962 Failed Matrix (Crack Saturation), Undamaged Fiber 3.0 Fiber Post-Failure Degradation Level 1 3.038 Fiber Matrix Post-Failure Degradation Level 2 ⋮

3.923 Fiber Post-Failure Degradation Level 25 3.962 Complete Fiber Failure

Plain Weave Composite Material Progressive Failure Analysis (activated) Pre-Failure Nonlinearity (not supported) Post-Failure Nonlinearity (not supported)

Energy-Based Degradation (not supported) Allowable


1.0 Undamaged Matrix, Undamaged Fiber 1.4 Fill matrix failure / unfailed warp 1.6 Warp matrix failure / unfailed fill 2.0 Matrix failure in warp and fill 2.2 Fill fiber and matrix failure / unfailed warp 2.3 Unfailed fill / warp fiber and matrix failure 2.7 Fill fiber and matrix failure / warp matrix failure 2.8 Fill Matrix Failure / warp fiber and matrix failure 3.0 Completely Failed


Unidirectional Composites

For unidirectional composite materials, state variables SDV2, SDV3, ..., SDV34 have the following interpretations: SDV2: SDV2 (often renamed as FI_MATRIX) is a continuous real variable that ranges from 0.0 to 1.0

and is used to indicate the fraction of the matrix failure criterion that that has been satisfied. For example, SDV2 = 0.0 implies that the matrix stress state is zero, while SDV2=1.0 implies that the matrix stress state has reached failure level. Numerically, SDV2 is computed as

SDV2 = ±Am1 ( )Im

12 − ±Am

2 ( )Im2

2 + Am3 Im

3 + Am4 Im

4 − ±Am5 Im

1 Im2

which is recognized as the left hand side of the matrix failure criterion (see Section 4 of the Helius:MCT Theory Manual).

SDV3: SDV3 (often renamed as FI_FIBER) is a continuous real variable that ranges from 0.0 to 1.0

and is used to indicate the fraction of the fiber failure criterion that that has been satisfied. For example, SDV3 = 0.0 implies that the fiber stress state is zero, while SDV3 = 1.0 implies that the fiber stress state has reached failure level. Numerically, SDV3 is computed as

SDV3 = ±A f1 ( )I f1 2 + A f

4 I f

4

which is recognized simply as the left hand side of the fiber failure criterion (see Section 4 of the Helius:MCT Theory Manual).

SDV4: SDV4 (often renamed as ETA_SM) is the fourth term in the matrix failure criterion and is used

in the pre-failure nonlinearity feature (see Section 4 of the Helius:MCT Theory Manual). SDV5: SDV5 (often renamed as ETA_NM or EFF_STNL_0) is used for post-failure calculations. If

Post-Failure Nonlinearity is activated, SDV5 is defined as (SDV2 – SDV4)/SDV2 and is used to determine if matrix cracking is present. If Energy-Based Degradation is activated, SDV5 is defined as a composite effective strain measure at fiber failure.

SDV6: SDV6 (often renamed as SIM_O or EFF_STSL_0) is used for post-failure calculations. If Post-

Failure Nonlinearity is activated, SDV5 is the composite average effective strain at the moment when the matrix failure criterion is triggered. If Energy-Based Degradation is activated, SDV5 is defined as a composite effective stress measure at fiber failure.

SDV7: SDV7 (often renamed as EFF_STNL) is a measure of the progress of degradation of the

composite after a fiber failure event. If Energy-Based Degradation is not activated, SDV7 is not used.

SDV8: SDV5 (often renamed as EFF_STNT_0) is defined as a composite effective strain measure at

matrix failure. If Energy-Based Degradation is not activated, SDV8 is not used. SDV9: SDV6 (EFF_STST_0) is defined as a composite effective stress measure at matrix failure. If

Energy-Based Degradation is not activated, SDV9 is not used. SDV10: SDV7 (often renamed as EFF_STNT) is a measure of the progress of degradation of the

composite after a matrix failure event. If Energy-Based Degradation is not activated, SDV7 is not used.


For the case of unidirectional composites, the remaining MCT state variables are used to store the individual components of the matrix average stress and strain states and the fiber average stress and strain states. SDV11: SDV12:

σm11

SDV13: σ

m22

SDV14: σ

m33

SDV15: σ

m12

SDV16: σ

m13

SDV17: σ

m23

SDV18: σ

f11

SDV19: σ

f22

SDV20: σ

f33

SDV21: σ

f12

SDV22: σ

f13

SDV23: σ

f23

SDV24: ε

m11

SDV25: ε

m22

SDV26: ε

m33

SDV27: ε

m12

SDV28: ε

m13

SDV29: ε

m23

SDV30: ε

f11

SDV31: ε

f22

SDV32: ε

f33

SDV33: ε

f12

SDV34: ε

f13

ε

f23

Woven Composites

For woven composite materials, state variables SDV2, SDV3, ..., SDV90 have the following interpretations: SDV1: See previous description of SDV1. SDV2: SDV2 (also known as FI_FILL_MATRIX) is a continuous real variable that ranges from 0.0 to

1.0 and is used to indicate the fraction of the matrix failure criterion that that has been satisfied for the matrix constituent within the fill tows.


SDV3: SDV3 (also known as FI_FILL_FIBER) is a continuous real variable that ranges from 0.0 to 1.0 and is used to indicate the fraction of the fiber failure criterion that that has been satisfied for the fiber constituent within the fill tows.

SDV4: SDV4 (also known as FI_WARP_MATRIX) is a continuous real variable that ranges from 0.0

to 1.0 and is used to indicate the fraction of the matrix failure criterion that that has been satisfied for the matrix constituent within the warp tows.

SDV5: SDV5 (also known as FI_WARP_FIBER) is a continuous real variable that ranges from 0.0 to

1.0 and is used to indicate the fraction of the fiber failure criterion that that has been satisfied for the fiber constituent within the warp tows.

SDV6: Not Used

For the case of woven composites, the remaining MCT state variables are used to store the individual components of the average stress and strain states in the various superconstituents and constituents (e.g., fill = fill tow superconstituent, warp = warp tow superconstituent, matrix-pocket = matrix constituent of the intertow matrix pockets, fill-matrix = the matrix constituent of the fill tow, warp-matrix = the matrix constituent of the warp tow, fill-fiber = the fiber constituent of the fill tow, warp-fiber = the fiber constituent of the warp tow. SDV7: SDV8:

σfill11

SDV9: σfill

22

SDV10: σfill

33

SDV11: σfill

12

SDV12: σfill

13

SDV13: σfill

23

SDV14: σwarp

11

SDV15: σwarp

22

SDV16: σwarp

33

SDV17: σwarp

12

SDV18: σwarp

13

SDV19: σwarp

23

SDV20: σmatrix-pocket

11


22


33


12


13


23

SDV26: σfill-fiber

11

SDV27: σfill-fiber

22

SDV28: σfill-fiber

33 σfill-fiber

12


SDV29: SDV30:

σfill-fiber13

SDV31: σfill-fiber

23

SDV32: σfill-matrix

11


22


33


12


13


23

SDV38: σwarp-fiber

11

SDV39: σwarp-fiber

22

SDV40: σwarp-fiber

33

SDV41: σwarp-fiber

12

SDV42: σwarp-fiber

13

SDV43: σwarp-fiber

23

SDV44: σwarp-matrix

11


22


33


12

SDV48: σwarp-matirx

13


23

SDV50: εfill

11

SDV51: εfill

22

SDV52: εfill

33

SDV53: εfill

12

SDV54: εfill

13

SDV55: εfill

23

SDV56: εwarp

11

SDV57: εwarp

22

SDV58: εwarp

33

SDV59: εwarp

12

SDV60: εwarp

13

SDV61: εwarp

23

SDV62: εmatrix-pocket

11


22


33


12


13 εmatrix-pocket

23


SDV67: SDV68:

εfill-fiber11

SDV69: εfill-fiber

22

SDV70: εfill-fiber

33

SDV71: εfill-fiber

12

SDV72: εfill-fiber

13

SDV73: εfill-fiber

23

SDV74: εfill-matrix

11


22


33


12


13


23

SDV80: εwarp-fiber

11

SDV81: εwarp-fiber

22

SDV82: εwarp-fiber

33

SDV83: εwarp-fiber

12

SDV84: εwarp-fiber

13

SDV85: εwarp-fiber

23

SDV86: εwarp-matrix

11


22


33


12

SDV90: εwarp-matirx

13 εwarp-matrix

23


Appendix E MCT State Variables for Cohesive Materials

The nine required state variables for Helius:MCT cohesive materials are defined below. They are represented in Abaqus/Viewer by SDVN where N is the unique integer which identifies the state variable (SDV1, SDV2, ... SDV9).

SDV1: The current damage state. This will be an integer between zero and 26. A value of zero indicates damage has not initiated yet. A value of 26 indicates complete failure (zero stiffness). Any other value indicates how much damage has been sustained. The states increment linearly starting at the effective displacement at damage initiation and ending at the effective displacement at complete failure. This state variable is used primarily as a tracking device for Helius:MCT. In order to observe damage it is recommended to view the damage variable (SDV6).

SDV2: A continuous real variable between zero and one which indicates how much of the damage initiation criterion has been satisfied. A value of zero indicates no loads (or only normal compressive loads) are acting upon the integration point and therefore are not satisfying the damage initiation criterion. A value of one indicates damage has initiated and the stiffness is reducing.

SDV3: The effective traction at damage initiation. The effective traction is defined as:

teff = { }tn

2 + ts2 + tt

2

SDV4: The effective displacement at damage initiation. The effective displacement is defined as:

δm = { }δn

2 + δs2 + δt

2

SDV5: The maximum effective displacement attained thus far in the loading history. The effective displacement is defined above.

SDV6: The damage variable, D, a continuous real variable between zero and one which indicates how much damage has occurred. A value of zero indicates zero damage has accumulated and the stiffness of the integration point has not degraded any. A value of one indicates a fully damaged material and consequently zero stiffness.

SDV7: The work done thus far in the normal loading mode (local 3-direction). Gn = ⌡⌠{ }tn dδn

SDV8: The work done thus far in the first shear loading mode (local 1-direction). Gs = ⌡⌠tsdδs

SDV9: The work done thus far in the second shear loading mode (local 2-direction). Gt = ⌡⌠ttdδt


Appendix F Troubleshooting

Appendix F.1 Manual Resolution of Keyword Conflicts produced by Abaqus/CAE

At any point during the creation of a finite element model, Abaqus/CAE permits the user to manually create keyword statements or modify existing keyword statements via the Keyword Editor. If the Keyword Editor is used to create or modify a particular keyword statement, then Abaqus/CAE no longer recognizes or manages that particular keyword statement. Consequently, any subsequent tasks that the user performs in Abaqus/CAE might possibly cause Abaqus/CAE to create new keyword statements which conflict with the keyword statements that were created or modified by the user via the keyword editor. These conflicting keyword statements will prevent Abaqus/Standard from completing the pre-processing phase of the finite element analysis. The conflicting keyword conflicts must be manually corrected by the user before Abaqus/Standard can be used to compute the finite element solution. In Step 13 of Section 3.1, the user chooses whether or not to allow the Helius:MCT GUI to change the default names of the MCT state variables to more descriptive names. If the user permits this action to occur, then the Helius:MCT GUI adds 6 new data lines to the *DEPVAR keyword statement as shown below: Original Modified Keyword Keyword

Statement Statement *DEPVAR *DEPVAR 6 6 1 MAT_STATE 2 FI_MATRIX 3 FI_FIBER 4 ETA_SM 5 ETA_NM 6 SIM_O

Even though this modification is performed by the Helius:MCT GUI, Abaqus/CAE treats this

modification as if it were performed by the user via the keyword editor. Consequently, Abaqus/CAE will no longer recognize the *DEPVAR keyword statement. In this case, the user must be cognizant of the possibility that Abaqus/CAE will create conflicting keywords in the input file.

One of the most common tasks that could cause Abaqus/CAE to generate conflicting keywords is the deletion of a Helius:MCT material definition from the model. If, prior to deleting the Helius:MCT material definition, the user allowed the re-naming of the MCT state variables, then Abaqus/CAE would no longer recognize the modified *DEPVAR keyword statement. Consequently, Abaqus/CAE would correctly delete the *MATERIAL and *USER MATERIAL keyword statements, but Abaqus/CAE would not delete the modified (i.e., unrecognized) *DEPVAR keyword statement. As a result, the model would contain an extraneous *DEPVAR statement that would conflict with any other Helius:MCT material definition that is created later.


Resolving Conflict Keywords

To access the model’s keywords in Abaqus/CAE, select Model Edit Keywords Model Name as shown in Figure F32.

Figure F32. The process of accessing the Keyword Editor in Abaqus/CAE

The Keywords Editor is shown in Figure F33. In the Keywords Editor, note the block of text that begins with “*Conflicts,

Generated keywords” and ends with “*Conflicts, End of conflict block”. These messages indicate that there is a keyword conflict contained within the block of text. In this case, the conflict is caused by the extraneous *DEPVAR statement that is left over from a Helius:MCT material that was deleted earlier.


Figure F33: Keywords Editor, showing a keyword conflict caused by an extraneous *DEPVAR statement

To manually resolve the keyword conflict, the user should delete the extraneous *DEPVAR statement (including all 12 of its data lines). The user must also manually delete both of the *CONFLICTS keyword statements. It should be emphasized that as long as there are user-modified keywords in the model, there is a possibility that new keyword conflicts will be generated as the user continues the model creation process in Abaqus/CAE. To completely eliminate the risk of introducing more keyword conflicts, the user can click the Discard All Edits button in the Keywords Editor. This operation will result in the reversion of all user-modified keyword statements to the form originally created by Abaqus/CAE. In this case, the user should be aware that any of the previous modifications made to the section definitions (see Section 3.3) will be lost.

Appendix F.2 System Error Codes

It is possible that an Abaqus analysis using Helius:MCT can crash in an unexpected manner resulting in Abaqus reporting a system error code within the .log file. The cause of the error may be from Abaqus or Helius:MCT and is a result of an undefined error during the analysis. Known causes of system error codes are listed below. The user should be aware that a specific error code number does not indicate a specific cause, as Abaqus reports a generalized system error code for multiple undefined errors. If the


user encounters unexpected behavior that they believe may be caused by Helius:MCT they are encouraged to contact Firehole support. System Error Code Possible Known Causes 5 A. Composite sections containing multiple Helius:MCT materials may cause

the program to crash unexpectedly during preprocessing. The specific cause is a varying number of requested state dependent variables (*DEPVAR keyword) throughout the layup. This problem occurs within Abaqus and is a known issue up through Abaqus 6.10. To alleviate the problem set all *DEPVAR values to the same number.

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