Computational Study of Cortical Bone Screw Pullout …€¦ · · 2012-09-05Department of Mechanical & Biomedical Engineering Computational Study of Cortical Bone Screw Pullout

Department of Mechanical & Biomedical Engineering

Computational Study of Cortical Bone

Screw Pullout Using the eXtended Finite

Element Method (XFEM)

Emer M. Feerick, J. Patrick McGarry

National University of Ireland Galway, Ireland

15th May, SCC 2012

Fracture in Abaqus

Two Methods Investigated:

1. Element deletion

– Voids nucleate and propagate as elements are

removed from mesh

2. eXtended finite element method (XFEM)

– no elements deleted from mesh

– Elements are split as crack propagates


Orthopaedic Screws

• Orthopaedic screws used for fracture

repair at sites throughout body

• Pullout failure mode reported clinically


Feerick et al, Computational Investigation of Metallic

and Carbon Fibre PEEK Fracture Fixation Devices for

Three-Part Proximal Humeral Fractures

Journal of Medical Engineering & Physics

(2012) under review

Experimental Testing

• Monotonic Tensile Pullout Test

• ASTM F543.23096-1

• Test Rate: 5mm/min

Longitudinal

Transverse

Load

Base

Plate

Cortical

Bone

Base

Clamp

Screw

Top

ClampOsteon

Alignment

* Feerick and McGarry, Cortical bone failure mechanisms during screw pullout, Journal of biomechanics (2012) article in press


Experimental Testing


Cortical Bone Microstructure Model

Longitudinal

Pullout SimulationTransverse

Pullout Simulation

Material 1 :

35% volume

Material 2 :

65% volume

Model Details

• Commercial screw geometry

• Screw-bone general contact

• COF 0.3

Cortical Bone Properties:

• Drucker Prager plasticity model

• Damage evolution

• Element deletion


Cortical Bone Plasticity

Drucker Prager Plasticity Model

– Pressure dependent yield

– Isotropic hardening

• Parameters*

– K = flow stress ratio

– β = friction angle

– Φ= Dilation angle

[*] Mercer et al, Acta Biomaterialia,2006; Mullins et al, JMBBM, 2009

d

β

t

p

Yield Surface

Damage Process

SIMULIA Abaqus 6.9 Manual

Damage Initiation

Shear Criterion

• Predict damage initiation due to shear

band localisation.

• Equivalent plastic strain at onset of

damage is a function of shear stress ratio

& strain rate

Criteria for Damage:


Damage Evolution

• Characteristic Length: L

• Linear damage evolution

• Damaged elements removed

from mesh (D=1)

1

D


Experimental Longitudinal Failure Mode

Initial Crack Initiation Crack

Progression

Final

Surface

Osteon Direction


Longitudinal Pullout Simulation


Transverse Failure Mode:

Initial

Peak

LoadCrack

Initiation

Final

Surface

Material

Detachment

Crack

Progress

Osteon Direction


Transverse Pullout Simulation


Limitations

• Mesh Sensitivity

– Larger elements mean larger voids


Limitations

• Unphysical over-closure between newly exposed

surfaces in highly deformed meshes.


Limitations

• Too computationally expensive for 3D microstructure

simulations


5.8 million

C3D4 Elements

Transverse 3D

Microstructure

Model

eXtened Finite Element Method (XFEM)

• Mesh Independent

• Enriched elements apply additional displacement

functions to selected regions of the mesh

• Contact can be applied between newly exposed

surfaces

• Abaqus 6.11 release contained UDMGINI which

facilitates anisotropic damage criteria to be defined

• Can not be used with axisymmetric elements


t

XFEM UDMGINI: Damage Initiation


• Anisotropic elasticity with anisotropic damage criteria

– Hashin damage tensile criteria (Index 1 & 2)

– Max principal stress criteria (Index 3)

1 (Fiber)

2 (Matrix) an

1 (fiber)

2 (Matrix)

Crack

1 (fiber)

2 (Matrix) Crackt

1 (fiber)

2 (Matrix)

anCrack

XFEM UDMGINI : Crack Propagation

• FNORMAL: Array of defining the normal

direction to the fracture line (2D) for

each failure index.

• Crack propagates based on energy

dissipation (*Damage Evolution)


Calibration for Cortical Bone

• Asymmetric 4PB

– Mode 2 / Mixed

Mode

• Symmetric 4PB / 3PB

– Mode 1


P P

c

b1b2

b1b2

Enrichment

Zone

* He and Hutchinson (2000) J. Appl. Mech.


• Simulations (Index 1&2) validated by experiments

– Crack Patterns

– Fracture Energy


Mode 1

Phase 0o

Mode 2

Phase 90o

*

*Osteon

Direction

Transverse

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 20 40 60 80 100

Gc

/G0

Phase Angle (o)

Experimental Zimmerman et al (2009)

XFEM UDMGINI

* Zimmerman et al (2009) j.biomaterials


• Introduce index 3

– Crack deviates from vertical


Mode 1

Phase 0o

*

Hashin Failure Index

Index 1&2

Mode 1

Phase 0o

Maximum Principal Stress

Index 1,2 & 3

* Zimmerman et al (2009) j.biomaterials

Application: 2D Screw Pullout


Osteon

alignment

Longitudinal

0 o

Osteon

alignment

Transverse

90 o

Osteon

alignment

45 o



Transverse

90 o45 oLongitudinal

0 o

Osteon

alignment



Pullout Force (Fp)

increases with increasing

osteon angle

Normalised Pullout

Force (Fp) versus

Pullout Force

Transverse (FpT)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 20 40 60 80 100

Fp

/ F

pT

Osteon Angle (o)

Feerick et al (2012)

2D XFEM

Transverse

90 o45 oLongitudinal

0 o

Osteon

alignment



• Investigate the effect of the helix

• And other unsymmetric features


Helical

Geometry

Cutting

Flute



Osteon Alignment

0 o

(Longitudinal)

Osteon Alignment

90 o

(Transverse)

Osteon

Alignment

Osteon Alignment

45 o

183,552 C3D4 Elements

Section 3Section 2

Section 2

Section 1



Section 3

Osteon Alignment

0 o

(Longitudinal)

Section 1

0 o

Section 2

Section 2

Section 1

Section 1



Section 3

Osteon Alignment

90 o

(Transverse)

Osteon Alignment

90 o

(Transverse)

90 o

Section 3

Section 2

Section 1



Section 3

Osteon Alignment

45 o

Section 1Section 2

Osteon Alignment

45 o

45 o



0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 20 40 60 80 100

Fp

/ F

pT

Osteon Angle (o)

Feerick et al (2012)

3D XFEM

0 o 90 o45 o

Pullout Force (Fp)

increases with increasing

osteon angle

Normalised Pullout

Force (Fp) versus

Pullout Force

Transverse (FpT)

Longitudinal

0 o

Osteon

alignment

Transverse

90 o

Summary

• XFEM predicts crack patterns compared to microstructure models

• Lower computational expense for 3D simulations


Microstructure

2D3D

XFEM

TransverseLongitudinal

3D

Documents

Computational Study of Cortical Bone Screw Pullout …€¦ · · 2012-09-05Department of Mechanical & Biomedical Engineering Computational Study of Cortical Bone Screw Pullout