FEA Information Engineering Journal September 2014 Information Engineering... · FEA Information Engineering Journal (FEAIEJ™) is a monthly published online journal to cover the

ISSN 2167-1273 Volume 3, Issue 9, September 2014

FEA Information Engineering Journal

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Aim and Scope FEA Information Engineering Journal (FEAIEJ™) is a monthly published online journal to cover the latest Finite Element Analysis Technologies. The journal aims to cover previous noteworthy published papers and original papers. All published papers are peer reviewed in the respective FEA engineering fields. Consideration is given to all aspects of technically excellent written information without limitation on length. All submissions must follow guidelines for publishing a paper, or periodical. If a paper has been previously published, FEAIEJ requires written permission to reprint, with the proper acknowledgement give to the publisher of the published work. Reproduction in whole, or part, without the express written permissio of FEA Information Engineering Journal, or the owner of of the copyright work, is strictly prohibited. FEAIJ welcomes unsolicited topics, ideas, and articles. Monthly publication is limited to no more then five papers, either reprint, or original. Papers will be archived on www.feaiej.com For information on publishing a paper original or reprint contact [email protected] Subject line: Journal Publication

Cover: Figure 4. Two opposing players Mild Traumatic Brain Injury-Mitigating Football Helmet Design Evaluation M.S. Hamid, Ph.D. - Advanced Computational Systems, LLC - Rochester, MI, USA. Minoo Shah, B.S.(Mechanical) - IDIADA Automotive Technology, Troy, MI.

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TABLE OF CONTENTS Publications are © to 13th LS-DYNA International Users Conference, 2014 Mild Traumatic Brain Injury-Mitigating Football Helmet Design Evaluation M.S. Hamid, Ph.D. - Advanced Computational Systems, LLC - Rochester, MI, USA. Minoo Shah, B.S.(Mechanical) - IDIADA Automotive Technology, Troy, MI. Batted-Ball Performance of a Composite Softball Bat as a Function of Ball Type Jennifer Yee1,2, James A. Sherwood1 and Stephen Fitzgerald2 1 Department of Mechanical Engineering, University of Massachusetts 1 University Ave. Lowell, MA 01854 USA 2 Combat, 20-5390 Canotek Road, Ottawa, Ontario, Canada, K1J 1H8 Breaking Bad(ly) – Investigation of the Durability of Wood Bats in Major League Baseball using LS-DYNA® Eric L. Ruggerio1, James A. Sherwood1 and Patrick J. Drane1 1Department of Mechanical Engineering, University of Massachusetts 1 University Ave. Lowell, MA 01854 USA ATV and MATV Techniques for BEM Acoustics in LS-DYNA Yun Huang, Zhe Cui

All contents are copyright © to the publishing company, author or respective company. All rights reserved.

3 Fea Information Engineering Journal September 2014

13th International LS-DYNA Users Conference Session: Simulation

Mild Traumatic Brain Injury-Mitigating Football Helmet Design Evaluation

M.S. Hamid, Ph.D.

Advanced Computational Systems, LLC Rochester, MI, USA.

and Minoo Shah, B.S.(Mechanical)

IDIADA Automotive Technology, Troy, MI.

ABSTRACT Concussion, as known as mild Traumatic Brain Injury (mTBI), is the most common sport-related head injury. Football is the most common sport with higher concussions in USA. Helmet is the equipment being used in mitigation of mTBI. There are numerous designs of helmets which meet the requirements of sport regulation committee. In this paper, a football helmet is evaluated using numerical methods. The brain and the tissues in human head are modelled using continuum Smoothed Particle Hydrodynamics (SPH). The brain tissues are generated by segmentation from human brain MRI data. The LSTC dummy is used to represent the football players. The brain tissue is fitted in the cavity of the dummy headform. Two different impact scenarios are simulated in this study. The results for these impact conditions are presented.

INTRODUCTION Concussion, as known as mild Traumatic Brain Injury (mTBI), is the most common sport-related head injury. Centers for Disease Control (CDC) estimates reveal 1.6 million to 3.8 million concussions occur each year in USA. Football is the most common sport with higher concussion risk due to the nature of the sport. A professional football player will receive an estimated 900 to 1500 blows to the head during a season. Impact speed of a football player tackling a stationary player is around 25mph. The topic of concussions and the effect that they have on the human brain are being increasingly scrutinized by media, political personnel and research community. Tremendous amount of research studies have been conducted by medical, defense and academic communities in understanding the etiology of concussion, treatment protocols and mitigation strategies by designing better equipment. Helmets are being developed and marketed in order to mitigate the mTBI. These helmets meet the requirements of the existing standards by National Operating Committee on Standards for Athletic Equipment (NOCSAE) [1]. Helmet testing to assess the impact performance is documented in Reference[2]. Impact test comparison of 20th and 21st century American football helmets is provides by Bartsch, et al[3]. The helmet designs vary widely. The designs are based upon simple inner foam padding, energy absorbing adapting head protection system, multi-directional protective systems, use of shear-thickening fluid layers,etc. The effects of pad composition, geometry and material stiffness were studied by Moss et al.[4]. Viano, et al studied the effect of mouthguards on head responses and mandible forces in football helmet impacts[5]. Externally applied foam is also used in football helmets for impact reduction [6].

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Session: Simulation 13th International LS-DYNA Users Conference

The numerical analysis of the human head models using the finite element technique is being used extensively for the past few decades. A literature review of the finite element human head models which are used in the medical and engineering fields is given by Samaka et al. [7]. Patient specific finite element head models are generated by Johnson Ho [8] based on Magnetic Resonance Imaging (MRI) scans. A multiscale computational estimation of axonal damage under inertial loading of the head was investigated by Wright et al.[9] using two dimensional finite element models of the head constructed from detailed MRI and Diffusion Tensor Imaging (DTI). Full-scale anthropomorphic test devices (ATD) that simulates dimensions and weight of the human body are being used in automotive crash testing and occupant protection modeling. The finite element model of ATD for impact analysis is available from Livermore Software Technology Corporation (LSTC). The brain that basically floats inside the skull is surrounded by cerebral spinal fluid. The head is subjected to linear acceleration and or a rotational acceleration during an impact or a blow. During the linear impact, the brain strikes the inner skull in acceleration and then hits the opposite side of the skull in deceleration and in the rotational acceleration scenario, the brain tissues are subjected to shear due to rotation of the head. In either case, the delicate neural pathways in the brain can become damaged, causing neurological disturbances. In this study, a generic helmet with foam padding is used in design evaluation for mitigation of brain injury. The brain geometry is developed from MRI image using segmentation technique. The brain is modeled using continuum SPH technique. The player is represented by H3 LSTC 50th percentile dummy.

METHODS BRAIN MODELING: A brain section is shown in Figure 1.

Sagittal Anterior Coronal

Figure 1. Brain Sectional Views

3D view of the brain tissue is obtained by segmentation of the MRI image using ITK-SNAP [10] program. The SPH model of the whole brain is shown in Fig. 2.

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Fig.2 MRI image and approximated SPH mesh.

The material model for approximated brain is assumed as viscoelastic material and the constants used in the analyses are:- Density = 1100 kg/m^3, Bulk Modulus = 500 MPa, G0 = 2.0MPa, Gi=1Mpa and Beta = 700/sec. HELMET MODEL: A generic helmet model is shown in Fig. 3.

Fig. 3 Helmet Model and Energy Absorbing Pads. The outer shell is modeled as plastic_kinematic material with Density=1200 kg/m^3, Young’s modulus = 1.50GPa, Yield Stress = 80MPa and Tangent Modulus =1.5 MPa. The energy absorbing pads are modeled as low density EPP foam with varying densities, Distribution of the foam is unsymmetrical and symmetric as shown in Fig 3. The symmetric foam model has some gaps between the skin and the foam pad as shown in the figure 3. PLAYERS MODEL 1: The players are modeled using LSTC ATD dummy as shown in Fig. 4

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Figure 4. Two opposing players. In this configuration, the opposing players are moving at 6.704 m/sec, a speed of 6.705m/sec. PLAYERS MODEL2: Both striking and the struck players are modeled using LSTC ATD dummy as shown in Fig. 5

Fig. 5. Struck player (left) hit by striking player (right).

The striking player velocity is 13.41 m/sec resulting in a speed of 30 mph.

RESULTS PLAYERS MODEL-1: The deformed configuration of the players and the neck deformation are shown in Fig. 6 and 7 for helmet model with gap between the skin and the foam pad. 1-4


Fig. 6 & 7 Left: Deformed configuration at 20.5 msec. Right: Neck deformation

Figs. 8 &9 Linear and Rotational resultant acceleration at CG of heads.

Fig. 10. Relative Rotation of the Head and Helmet.

The linear resultant acceleration and rotational acceleration are shown in Fig. 8 and 9 of the head for both left and right players. The peak resultant acceleration is of the order 800g. The rotational acceleration about Y axis is very high. Figure 10 shows the relative rotation of the head and the helmet. The peak pressure is 12MPa at maximum acceleration occurring time 13msec. 1-5


PLAYERS MODEL -1 _Updated Foam Geometry: The padding geometry is updated so that there is a good fit of the helmet with the head skin. The same impact scenario as the previous case is used in this study. The deformed configuration at 18msec is shown in Fig. 11. The head acceleration plot is shown in Fig. 12. The peak acceleration is 350g.

Fig 11. The deformed configuration shows upward movements of the helmets.

Figure 12. The resultant head acceleration

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Figure 13. Vertical displacement of the head and helmet

Fig. 14 Contours of effective strain distribution at 10msec .

Fig. 15. Contours of effective stress at 11msec.

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Figure 13 shows the vertical movement of the heads due to impact. The vertical displacement is 80-90mm and the neck rotation is high. The resultant head rotational acceleration is 30000 rad/sec^2. Figure 14 shows the strain distribution in brain tissue and is 0.0011. Figure 15 shows the contours of effective stress at 11msec and the peak value is 0.78MPa. PLAYERS MODEL2: The neck deformation is shown in figure 16. The head acceleration of the struck player is shown in Fig. 17. The peak acceleration is 240g. The effective strain in the brain tissue at 12msec is shown in Fig. 18. The strain is 0.000924.

Figure 16. The Head and Neck Deformation at 25 msec.

Figure 17. The head acceleration plot of struck player.

The shear stress distribution in the brain tissue at 12msec is shown in figure 19. The maximum shear stress is 0.48MPa.

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Figure 18. Effective strain distribution at 12msec in the brain tissue.

Figure 19. The shear stress distribution in the brain tissue at 12msec.

DISCUSSION AND CONCLUDING REMARKS The human brain model was developed using MRI images. The brain tissues and surrounding soft tissues were lumped as one material. The finite element modeling of these brain tissues were approximated as structural SPH particles. The players were represented by using existing ATD model from LSTC dummy library. A generic helmet was modeled in this study. The impact scenarios of two football players colliding with each other were presented. The first one was head on collision of two players at a velocity of 6.704 m/sec. The second one was a striking player running with a velocity of 13.4 m/sec impacting the standing stuck player. Two padding designs were studied. The first one was with the foam padding fully covered but not

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completely fitting with the head skin. In the second, the foam paddings were fitted so that they are in contact with the headform outer layer skin. In the first configuration of head on collision, the results showed high peak accelerations. Since the impact energy was high, the neck rotations were also high. The heads also moved upward in the process of dissipating the energy and this resulted in higher neck rotation. The peak acceleration for the second foam design tightly in contact with the head showed 350g compared to the first configuration where in the pads were not in tight fit. It is better to keep tight fit of the pads so that the energy absorption starts as soon as the impact takes place. In the second configuration, the striking player was moving at a high speed of 13.4 m/sec and the struck player was stationary. The striking player was hitting at an angle of 60 degrees. The peak acceleration induced was high and neck rotation was also high. All these simulations were run using the Linux 64 bit smp d R7.0.1 LS-DYNA version. The LS-PrePost version 4.1 was used in meshing and the post processing the results. A number of assumptions and approximations were made in these analyses. Mathematical modeling of biological tissues such as brain is complex because of wide variation in the geometry and unknown tissue properties. Some of these assumptions and approximations may not be exactly representing the actual structure or the product, however, the mathematical simulation provides insight in understanding the mechanics. Coupling the advancement in medical imaging technology with powerful computational tools such as LS-DYNA help evaluate and understand the brain injury mechanism in finding solutions for mitigation of mild traumatic brain injury. ACKNOWLEDGEMENT The authors wish to thank Mr. Dilip Bhalsod of LSTC for his technical help in running the DYNA jobs. Also, thanks to Dr. Zakir Sahul, M.D., in helping to understand some of the medical imaging programs and applications. References

1. Standard Test Method and Equipment Used in Evaluating the Performance Characteristics of Protective Headgear/Equipment, Prepared by NOCSAE- National Operating Committee on Standards for Athletic Equipment, July, 2013.

2. Pellman, E.J., Viano, D.C., Withnall,C., Shewchenko,N, Bir, C. and Halstead,P.D., ‘Concussion in Professional Football: Helmet Testing to Assess Impact Performance – Part 11’, Neurosurgery, Vol. 58, 78-96, January 2006.

3. Bartsch,A., Benzel,E., Miele,V. and Prakash V., ‘ Impact test comparison of 20th and 21st century American football helmets’, J. Neurosurg., Number 4.,2011.

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4. Moss,W.C., King, M.J. and Blackman E.G., ‘Toward reducing impact brain injury: Lessons from computational study of army and football helmet pads’, LLNL-JRNL-490182-Draft.

5. Viano, D.C., Withall,C. and Wonnacott,M., ‘Effect of mouthguards on head response and mandible forces in football helmet impacts’, Annals of Biomedical Engineering, Published online: 13 October 2011.

6. Vilar-Carrasquillo, L.D. and Anderson, B.E., ‘ Impact reduction in football helmets due to application of externally applied foam’, Los Alamos National Laboratory, LA-UR-13-26665, August, 2013.

7. Samaka, H. and Tarlochan,F, ‘Finite element (FE) human head models/Literature Review’, Intl. J. of Scientific & Technology Research, Vol. 2, Issue 7, July 2013.

8. Johnson Ho, ‘ Generation of patient specific finite element head models’, Doctoral Thesis, KTH Royal Institute of Technology, Stockholm,Sweden, 2008.

9. Wright, R.M. Poat, A., Hoshizaki,B. and Ramesh, K.T., ‘ A multiscale computational approach to estimating axonal damage under inertial loading of the head’, J. of Neurotrauma, Vol. 30, 102-118, Jan. 2013.

10. Yushkevich,P.A., Piven,J., Hazlett,H.C., Smith, R.G., Ho,S., Gee, J.C. and Guido Gerig. ‘User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability’. Neuroimage 2006 Jul 1;31(3):1116-28.

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Batted-Ball Performance of a Composite Softball Bat as a Function of Ball Type

Jennifer Yee1,2, James A. Sherwood1 and Stephen Fitzgerald2

1 Department of Mechanical Engineering, University of Massachusetts 1 University Ave. Lowell, MA 01854 USA

2 Combat, 20-5390 Canotek Road, Ottawa, Ontario, Canada, K1J 1H8

Abstract Experimental and finite element methods were used to model the collision between a composite softball bat and softballs of different COR (Coefficient of Restitution) and compression specifications. Experimental bat characterization methods included barrel compression and modal analysis. Experimental softball characterization methods included COR, CCOR (Cylindrical Coefficient of Restitution), compression and dynamic stiffness. Finite element models were built in HyperMesh and analyzed in LS-DYNA®. Softballs were modeled using material models #6, #57 and #83, and the composite softball bat was constructed according to the manufacturer’s specifications using *PART_COMPOSITE. Three methods to calibrate the finite element softball models were investigated and included “flat-surface” and “cylindrical-surface” coefficients of restitution and DMA (dynamic mechanical analysis). The “cylindrical-surface” test was found to be the most effective method of calibration to predict the batted-ball speed (BBS) as measured in bat/ball impact testing.

Introduction

In the early 2000s, composite bats gained broad attention in the softball community when some bat manufacturers produced bats that significantly outperformed the best aluminum bats on the market. One composite bat performed so well that the ASA (Amateur Softball Association) quickly banned it and threatened to ban all composite bats as this governing body had done with the titanium bats in 1993. However, before taking such drastic action, the ASA revisited its process for imposing limits on the performance of softball bats [1]. Today, bats used in ASA championship play must be certified to be in compliance with performance regulations at an ASA-Approved testing facility [2]. However, even with restrictions that place aluminum bats and composite bats on a “level playing field” with respect to batted-ball performance in the certification test, composite bats have become the bat of choice for a majority of softball players.

Finite element (FE) modeling has been used in sports ball simulations such as cricket, baseball, tennis and golf [3-6]. A good finite element model that can accurately predict bat-ball performance is an extremely valuable tool to assist in the design of a bat, as it reduces the need for labor intensive, time consuming and expensive experimental prototyping and testing. Particularly with composite layups, any number of combinations of materials and ply angles can be explored using the model, which would otherwise take weeks to explore using a prototype testing program.

A credible finite element model of the ball-bat collision for softball is challenging. Achieving such a model is difficult primarily because of variations in the processing of the softballs’ polyurethane cores which can yield different properties of the overall ball, e.g. hardness and liveliness, and the response of the softball during a bat-ball collision is rate dependent. The

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mechanical behavior of the composite bat is slightly less challenging to model because the bat material can be assumed to be essentially linear elastic unless significant material damage is induced during the collision. The ideal models should have the flexibility to allow for changes in bat and ball constructions and have the ability to capture how BBS varies as a result of these changes. If such models were available, then one could customize the bat design with the goal to maximize the BBS for a given ball construction.

This paper presents a summary of the complimentary experimental and finite element studies that were completed to develop a bat-ball collision model for the research of composite softball bats. Softballs were characterized using simple tests, and finite element models of the softballs were calibrated to yield good correlation to the experimental characterization tests. The calibrated softball models were then used to explore their ability to correlate with bat-ball collisions using a composite softball bat.

Experimental Methods Two types of softballs and one composite bat were investigated using experimental methods. Softball characterization data were used to find material constants for finite element models of the softballs. The composite bat data were used to demonstrate the credibility of the finite element model of a composite softball bat that was built using ply layup information from the bat manufacturer. Bat performance data were collected for subsequent comparison to finite element simulations of bat/ball impacts to explore how well independent calibration of bat and ball models could work as a predictive design tool.

Ball Compression Testing

Testing for softball compression was conducted in accordance to ASTM F1888-09 [7]. Softballs were compressed between two flat surfaces and oriented such that the plates contacted between the seams as shown in Figure 1 to a displacement of 0.25 in. at a rate of 1 in/min. The force required to displace the ball the prescribed distance was recorded, the ball was rotated 90°, and compressed again. The average of the two forces was recorded as the compression load for the softball.

Figure 1. Softball compression test setup.

Ball COR/CCOR and Dynamic Stiffness Testing

Testing was conducted to determine the COR, CCOR and the DS of the softballs using the test setup shown in Figure 2. The flat impact surface used in the testing is a 3 x 4 in. x 1-in. thick steel plate, and the cylindrical impact surface is a 2.63-in. diameter half cylinder. The impact plate is mounted on three piezoelectric load cells that measure the forces during impact at a rate of 105 samples per second. A ball carrier called a “sabot” shown in Figure 3 is used to fire the

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ball and ensures the ball impacts the plate between the seams and without spin. The sabot impacts the arrestor plate, and the ball travels through the three light gates.

Figure 2. Dynamic stiffness test setup. Figure 3. Softball loaded in a ball carrier, or "sabot.”

Bat Barrel Compression

Bat barrel compression testing was done to quantify the stiffness of the barrel section of the softball bat. The test setup used is shown in Figure 4. The bat is placed in the fixture and compressed between two 3.86-in. diameter steel half-cylinder platens at the 6-in. location as measured from the endcap. The hand crank shown in the figure rotates to displace the bottom platen and compress the barrel.

Figure 4. Barrel compression test setup.

First, an initial preload of 5-15 lb. is applied to the barrel, and both gauges are zeroed to establish the reference, or zero displacement point. The barrel is then compressed 0.02 in., the force is recorded, and the gauges are zeroed again. The barrel is compressed an additional 0.05 in. where the force is measured a final time. The force required to displace the barrel the first 0.02 in. is referred to as the “preload” and the force to compress it the final 0.05 in. is referred to as the “final load”. The bat is then rotated a prescribed amount, and the process is repeated. The barrel compression is the average of the final loads at the 0°, 90°, 45° and -45° orientations. Modal Analysis

Impact modal analysis was done on the composite softball bat to determine the first two bending and hoop frequencies. The bat was suspended from the ceiling using two strings to simulate a free-free condition as shown in Figure 5. Two accelerometers were attached approximately 90° from each other 1 in. from the endcap as shown in Figure 5. 1-3


Figure 5. Modal test setup of a simulated free-free condition with accelerometers attached

90° from each other to measure the bending and hoop frequencies of the bat.

The bat was impacted with a plastic-tip force hammer, on the opposite side of one of the accelerometers as shown in Figure 5. The impulse and accelerometer data were collected by a Dactron Photon II four-channel FFT analyzer, and the RT Pro Photon data acquisition program analyzed the frequency response. The frequency range of 1000 Hz with 800 spectral lines of resolution was used to determine the first two bending modes, and the range was increased to 2000 Hz to determine the first two hoop modes. The frequency response function (FRF) was computed from the time response using the Fast Fourier transform based on the ratio of acceleration output to force input [8].

The natural frequencies were determined using a “peak pick” technique on the FRF response function. The bending frequencies are the first peaks to occur, and the hoop frequencies are indicated when the response functions from each of the accelerometers overlay each other with the same magnitude. A typical FRF for a hollow baseball bat showing the first three bending and first two hoop modes is shown in Figure 6 [8].

Figure 6. FRF measurement from a hollow baseball bat, displaying three bending modes and two hoop modes [8].

Batted-Ball Speed

The batted-ball speed (BBS) is found in a controlled lab test and is used to determine the relative performance of the different softballs on the composite softball bat. The air cannon shown in Figure 7 was used for this testing. The bat is held stationary at the start of the test and is able to pivot about the 6-in. location as measured from the base of the knob. The ball is fired at the barrel 6 in. from the endcap, and the inbound and outbound velocities are measured by three light gates. Testing was performed at 95 and 110 mph. Balls are fired using a sabot in the same configuration as the dynamic stiffness testing. The cannon was controlled by a LabVIEW program on the computer shown in Figure 7, and the program displays the inbound and outbound velocities. The inbound and outbound velocities are used to calculate the BBS of the bat and ball combination.

Impact side Accelerometers

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Figure 7. LVS sports cannon configuration.

Modeling This section discusses the methods used for the finite element models of the softballs and bats for analysis in LS-DYNA. Models were built in HyperMesh v11.0 and analyzed in LS-DYNA version 971 R6.0.0 using double precision. It was found that using flat wall COR data to calibrate the material parameters of the ball did not translate as well as CCOR calibration for predicting batted-ball speeds. Thus, only the CCOR ball modeling is reported in this paper.

Construction of the Softball Finite Element Model

Softballs were modeled as an isotropic, homogeneous sphere with 12096 eight-noded solid elements and used Material Models #6 General Viscoelastic, #57 Low-Density Urethane Foam, and #83 Fu-Chang Foam with Rate Effects. The default constant-stress reduced-integration solid elements were used. LS-DYNA notes that when large deformation is seen in the elements, such as in a CCOR test or bat-ball collision, the one-point reduced integrated elements are more robust than the fully integrated twenty-noded solid elements and can reduce hourglassing in the model [9]. CCOR Models

The cylindrical impact surface for the CCOR model was meshed with 2664 solid elements. The target is defined as a rigid material using Material Model #20, and all nodes are constrained in translation and rotation in the material card. An example CCOR model with boundary conditions and the global axis used are shown in Figure 8. The explicit solver was used for completing the impact analyses.

Ball Compression Model

The ball compression models were conducted using implicit analysis due to the relatively slow speed at which compression tests are performed. The compression plates are defined as rigid bodies with Material Model #20 and meshed with 2000 elements each as shown in Figure 9. The bottom plate (blue) is fixed in translation and rotation, and the top plate is given a prescribed velocity of 0.02 in/sec. The time period for the analysis is 14 sec., and the compression value of the ball is determined by the force associated with a 0.25-in. displacement. The contact option

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*AUTOMATIC_SURFACE_TO_SURFACE was used to define the interaction between the ball and the plates.

Figure 8. Example CCOR model with boundary

conditions.

Figure 9. Softball compression test. The bottom (blue) plate is fixed, while the top (red) plate is

given a prescribed velocity to compress the ball. Construction of the Composite Bat Finite Element Model

For the current research, the authors were fortunate to have the manufacturer provide the details of the ply layup for a double-wall composite softball bat. The composite softball bat model was built with 20494 four-noded thin shell elements. *PART_COMPOSITE was used to define the angle, thickness and material of each layer in the laminate. The bat is comprised of braided layers of glass and carbon fibers. Each braided ply is defined in the model using a [+/-/+/-/+] configuration, where the “+” layers each have 1/6th of the total thickness of the ply, and each “-” layer has 1/4th of the total thickness of the ply. Defining each braid layer of the bat in this manner eliminates the bending/extensional coupling that occurs in a non-symmetrical laminate stack-up [10]. The bat was partitioned into ten components including the knob and endcap because the number of plies and angles vary along the length of the bat due to the differences in diameter in the handle, taper and barrel sections. The knob and endcap are fixed to the handle and barrel, respectively, with merged coincident nodes.

Material model #22 was used for each layer of the laminate where the density, Poisson’s ratios, Young’s Moduli, and shear moduli are defined. The local material axis was defined using the AOPT = 3 option for orthotropic materials. The material axis option allows the model to account for the change in the orientation of the surface normal with respect the global reference frame due to the cylindrical shape of the bat.

In the case for thin shell elements as used in this research, the normal is always perpendicular to the plane of the element. The orientation angle for any given ply of the laminate was defined locally for each element using the *ELEMENT_SHELL_BETA card which is a rotation in the plane of the element from the vector a = v x n.

The “double-wall” part of the bat refers to a 10-in. long tube (insert) that is pressed into the barrel of the bat, with a 0.001-in. interference fit. The contact definition between the barrel and insert was defined as *INTERFERENCE_SURFACE_TO_SURFACE contact. Dynamic relaxation (DR) was used to introduce the pre-stressed state of the interference fit in the barrel section. This method uses a “pseudo” analysis that is performed quasi-statically either implicitly or explicitly before the transient analysis. During the pseudo analysis, the interference is gradually eliminated by scaling the contact thickness from zero to a maximum value of unity [11]. The interface stiffness is scaled from zero to unity during the DR phase with a load curve

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(LCID1) defined in the contact definition, and this stiffness is held constant during the transient phase with a second load curve (LCID2) [12].

During the pseudo analysis, the ratio of current to peak kinetic distortional energy is monitored, such that the pseudo phase terminates when the ratio falls below the user-defined convergence tolerance (DRTOL) [12]. This stressed state then becomes the initial state for the subsequent transient analysis. The DR phase can be seen graphically in the binary output “d3drlf” file as shown in Figure 10. At the conclusion of the DR phase, a prescribed geometry file (drdisp.sif) is written. This file is utilized by setting IDRFLAG = 2 in subsequent analyses to invoke the prestressed state without having to repeat the DR convergence [12].

Figure 10. Example von Mises stress fringe plot during the dynamic relaxation

pseudo phase for the barrel of the bat. Stress units are psi. Barrel Compression

The barrel compression model was solved using the implicit solver. As shown in Figure 11, the barrel was modeled between two rigid half-cylinder platens each with a diameter of 3.3 in. and meshed with 8960 solid elements. The bottom platen was fixed for translation and rotation. The top platen was only permitted to translate in the y-direction and was given a prescribed velocity of 3.5x10-3 in/sec to compress the barrel 6 in. from the endcap.

The circumferential nodes on the barrel and insert were constrained so as not to allow translation in the x-direction, and the four nodes that lie on the y-axis were constrained in the z-direction to ensure the bat does not slip while it is being compressed. The boundary conditions are shown in Figure 11 and Figure 12.

The *AUTOMATIC_SURFACE_TO_SURFACE contact was used to define the interaction between the platens and barrel. The force to displace the barrel was extraxcted from the ascii file rcforc, and the displacement of the barrel was determined from the binary time history plot. The time period for the analysis was 25 sec., and the force vs. displacement was plotted to determine the barrel compression. The interfacial forces between the inside of the barrel and the insert were also of interest. The insert was meshed into two components as shown in Figure 13 to observe the forces from the “top” of the barrel and the “bottom” of the barrel separately.

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Figure 11. Barrel compression model configuration with boundary

conditions (x-y view).

Figure 12. Barrel compression model configuration with boundary conditions

(y-z view).

Figure 13. Insert inside barrel meshed into two components.

Modal Analysis Model

A free-free modal analysis was completed using LS-DYNA as a method to calibrate the finite element model of the softball bat model to correlate with the physical bat. The goal was to correlate the first two bending and hoop modes. The analysis was completed using the implicit solver. Thirty modes were extracted to ensure the first and second bending and first and second hoop modes were found during the analysis.

Batted-Ball Performance Model

In the batted-ball performance testing model, the composite bat was supported by an aluminum pivot which was meshed with 17891 reduced-integration solid elements as shown in Figure 14. The *AUTOMATIC_SURFACE_TO_SURFACE contact definition was used to define the interaction between the pivot and the bat. The pivot has a single node measured 6 in. from the base of the knob that is fixed in translation and rotation. This boundary condition keeps the bat stationary until it is impacted with the ball, then allows for rotation after the impact. The ball was given an initial velocity when fired at the bat. The contact between the ball and bat was also defined as *AUTOMATIC_SURFACE_TO_SURFACE. The time period for the modeling of

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the bat-ball impact was 0.002 sec. to ensure the ball has reached a steady-state velocity after the impact.

Figure 14. Bat-ball finite element models for a composite softball bat.

Ball Material Model

A softball is made of a polyurethane core wrapped in a leather cover. As a result, the ball behavior is viscoelastic where the deformation and energy dissipation are a function of the rate and state of deformation. A number of the viscoelastic material models that are available within LS-DYNA were explored for the modeling of the ball. The material models considered included #6 Viscoelastic, #57 Low-Density Urethane Foam, and #83 Fu-Chang Foam with Rate Effects. For this research, Material Model #6, often called the Power Law model [13], was found to give the best correlation with experimental data.

Results Physical Properties

Table 1 compares the experimental and finite element results for the weight, MOI (Mass Moment of Inertia) and Balance Point of the 33.1-in. long composite bat. Each of the categories shows good correlation between the model and experimental values. The MOI shows a 1.4% difference from experiment.

Table 1. Experimental and finite element results for bat physical properties.

Weight (oz.) MOI (oz-in2)

Balance Point (in. from base of the knob)

Exp. FE Exp. FE Exp. FE 22.1 22.1 6920 7020 21.0 21.0

Barrel Compression

Table 2 lists the experimental and finite element barrel compression results for the composite softball bat with the insert. The preload is the force associated with the first 0.02-in. displacement, and the final load is the force associated with the additional 0.05-in. displacement. After the preload is applied, the force is “zeroed” out and is presented this way in Table 2. The experimental values listed are the averages of the compression values at the four barrel orientations.

Table 2. Experimental and finite element composite barrel compression results

Method Preload (lbs.) Final Load (lbs.) Experiment 186 368

FE 155 386

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The bat finite element model shows excellent correlation to experimental data, as the final loads are within 5% between the model and the experiment. The finite element model of the bat can be justified to have a higher barrel stiffness than the experiment because the model assumes perfect bonding between plies, and thus, does not consider flaws or any variations in ply orientations which can occur during manufacturing [10]. Even without this rationalization for the slight difference between the experimental and finite element compression values, this correlation is remarkable and infers that the finite element model of the bat is an excellent representation of the physical bat. Modal Analysis

Table 3 shows the experimental and finite element model results of the free-free modal analysis. The first two bending and hoop modes are compared. All modes show reasonably good correlation between the model and the experimental data. Because the finite element model of the bat showed such good agreement to the experimental MOI and BP, no adjustments were made to the mass distribution to assist in improving the correlation to the bending frequencies. The stiffness of the handle was also shown to influence the bending frequencies, however to preserve the manufacturer’s composite layup specifications, the material definitions were not altered.

Table 3. Composite softball bat experimental and finite element free-free modal analysis results

Method 1st Bending (Hz) 2nd Bending (Hz) 1st Hoop (Hz) 2nd Hoop (Hz) Experiment 146 555 1450 1950

FE 126 468 1406 2086 Ball Calibration: “Cylindrical-Surface” Calibration

Two softball types were used in the experimental CCOR/DS testing and are likewise referenced as Ball Types 1 and 2. Material model #6 parameters as determined through parametric studies for each ball model are given in Table 4. Table 5 outlines the experimental and FE results for Ball Types 1 and 2 CCOR testing at 95 and 110 mph. The percent difference from experiment is also shown. Table 4 shows the experimental and FE results for Ball Types 1 and 2 DS testing at 95 and 110 mph. The results indicate the DS is underestimated by the FE model, with the Ball Type 1 model showing a 14% difference at 95 mph, and an 8% difference at 110 mph. The Ball Type 2 model showed a 20% difference at 95 mph and a 14% difference at 110 mph. The peak loads and contact times were also compared, and the results are shown in Tables 7 and 8. The experimental and FE force vs. time curves are also compared in Figure 15. The FE ball model shows better agreement to the peak loads than the DS. The model also shows reasonable correlation to the contact time seen in experiment. The results in Table 8 show that experimental contact time for Ball Type 2 is approximately 0.2 ms longer than Ball Type 1, which is likely a result of the lower compression and the lower dynamic stiffness of Ball Type 2. It is recommended that an “automated” optimization study be pursued in the near future to explore the ability to achieve a better correlation between the model results and the experimental data.

Table 4. Material model #6 parameters used for cylindrical surface calibration for ball types 1 and 2.

Ball Type K (psi) G0 (psi) G∞ (psi) β 1 800000 22500 750 75000 2 100000 11000 640 60000

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Table 5. Ball types 1 and 2 experimental and FE results for CCOR at 95- and 110-mph

Ball Type

95-mph CCOR 110-mph CCOR

Exp. FE

% Difference Exp. FE

% Difference Material Model CCOR Material

Model CCOR

1 0.380 6 0.381 0.26 0.355 6 0.368 3.66 2 0.460 6 0.456 0.87 0.442 6 0.439 0.68

Table 6. Experimental and FE results for DS at 95- and 110-mph

Ball Type

95-mph DS 110-mph DS

Exp. (lb/in)

FE % Difference

Exp. (lb/in)

FE % Difference Material

Model DS

(lb/in) Material Model

DS (lb/in)

1 7190 6 6153 14.40 7260 6 6680 8.06 2 5760 6 4610 20.0 5780 6 4980 13.76

Table 7. Experimental and FE results for peak loads at 95- and 110-mph

Ball Type

95-mph CCOR Peak Load 110-mph CCOR Peak Load

Exp. (lbs.)

FE % Difference Exp.

(lbs.)


Model Load (lbs.)

Material Model

Load (lbs.)

1 4700 6 4390 6.36 5540 6 5300 4.46 2 4150 6 3690 11.05 4780 6 4440 7.00

Table 8. Experimental and FE results for contact time at 95- and 110-mph

Ball Type

95-mph CCOR Contact Time 110-mph CCOR Contact Time

Exp. (ms)

FE % Difference Exp.


Model Time (ms)

Material Model

Time (ms)

1 1.03 6 1.20 16.50 1.01 6 1.09 7.92 2 1.21 6 1.40 16.50 1.20 6 1.30 8.33

Figure 15. Ball Type 2 force vs. time. (a) 95-mph CCOR and (b) 110-mph CCOR.

Batted-Ball Speed Using Calibrated Softballs and Composite Bat

Next, the “cylindrical-surface” calibrated softball models were fired at the 6-in. location on the composite softball bat. The BBS results are listed in Table 9. The experimental results for Ball Type 1 showed a slight increase (0.50 mph) in BBS at the higher test speed for impacts with the

(b) (a)

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composite bat. Ball Type 2 shows relatively good correlation to the BBS but underestimated the BBS by 5% at 95 mph and 3% at 110 mph. Also, the experimental results for Ball Type 2 showed a decrease of 2.06 mph from the 95 to 110 mph test speed. This decrease was able to be captured by Material model #6, while on a smaller scale of 0.045 mph. This slight reduction for the model is not shown in the table due to rounding of the speeds to the nearest 0.1 mph.

Table 9. Ball types 1 and 2 experimental and FE performance results for impacts

with the composite bat at 95 mph and 110 mph

Ball Type

95-mph BBS 110-mph BBS

Exp. (mph)

FE % Difference

Exp. (mph)


Model BBS

(mph) Material Model

BBS (mph)

1 96.5 6 95.8 0.74 97.0 6 97.2 0.37 2 95.2 6 90.1 5.40 93.2 6 90.1 3.35

Conclusions

Experimental characterization of a softball bat and softballs of different COR and compression specifications were conducted. Complementary finite element models were constructed in HyperMesh, analyzed in LS-DYNA and were manually tuned to give reasonable correlation with the experimental test data. The modal and barrel compression behaviors of the bat were studied. Reasonable correlation was achieved for bat ball collisions. However, future work to use a more sophisticated method to conclude the material parameters is recommended.

Acknowledgement

The authors appreciate the expertise and financial support provided by Combat Sports for the pursuit of this research.

References

1. Russell, D.A. Are Composite Bats better than Aluminum Bats? 2005. 2. ASA, ASA Bat and Ball Certification Program. 2004: Oklahoma City, Oklahoma. 3. Singh, H., Experimental and Computer Modeling to Characterize the Performance of Cricket Bats, in School of

Mechanical and Materials Engineering. 2008, Washington State University: Pullman, WA. 4. Mustone, T.J., and Sherwood, J.A. Using LS-DYNA to Characterize the Performance of Baseball Bats. in

Proceedings of the 5th International LS-DYNA Users Conference. 1998. Southfield, MI. 5. Widing, M.B., Moeinzadeh, M.H., Finite Element Modeling of a Tennis Racket With Variable String Patterns

and Tensions. Journal of Applied Biomechanics, 1990. 6(1): p. 79-91. 6. Mase, T., Experimental Benchmarking Golf Ball Mechanical Properties in SEM X International Congress &

Exposition on Experimental & Applied Mechanics. 2004. 7. ASTM, F1888-09: Standard test method for compression-displacement of baseballs and softballs. 2012. 8. Sutton, A.D., Using Modal Analysis to Investigate Bat-Ball Performance of Baseball Bats, in Mechanical

Engineering. 2008, University of Massachusetts at Lowell Lowell, MA. 9. LSTC. Ls-Dyna Support Site - Negative Volume in Brick Elements. 2012. 10. Hyer, M.W., Stress Analysis of Fiber-Reinforced Composite Materials. 1998: WCB McGraw-Hill 11. Bala, S., Stress Initialization in Ls-Dyna, LSTC, Editor. 12. LSTC, LS-DYNA Keyword Manual Version 971 R.6.0.0. 2012. 13. LSTC, LS-DYNA Keyword User's Manual - Volume II Material Models 2012.

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Breaking Bad(ly) – Investigation of the Durability of Wood Bats in Major League Baseball using LS-DYNA®

Eric L. Ruggerio1, James A. Sherwood1 and Patrick J. Drane1

1 Department of Mechanical Engineering, University of Massachusetts

1 University Ave. Lowell, MA 01854 USA

Abstract The bats used in Major League Baseball (MLB) are turned from a single piece of wood. Northern white ash had been the wood of choice until the introduction of hard rock maple in the late 1990s. Since the introduction of maple, there has been a measurable increase in the number of bats breaking into multiple pieces. These failures can be a significant factor during play, i.e. pieces of bats landing flying into the field of play, thereby distracting fielders from making the appropriate play for the given game situation. Observations of bat breakage in the field and in controlled conditions of lab testing of bats have shown the bat durability is a function of wood quality and bat profile. Wood quality is described by the density and the slope of grain of the wood. The bat profile is described by the variation in the diameter of the bat along its length. The bat properties that are preferred by players, i.e. low-density wood and a bat profile of a big barrel and a slender handle, are in direct contradiction with what makes for a durable bat. In this paper, LS-DYNA is used to develop calibrated models of the breaking of yellow birch wood bats in controlled lab conditions. The WOOD material model in combination with the ADD EROSION option using a maximum principal strain failure criterion was found to produce a credible simulation of the failure modes seen in wood baseball bats.

Introduction

In the early years of the baseball, bats were made from a large variety of wood species. White ash became the wood of choice in the late 19th century after the Hillerich family in Louisville, Kentucky manufactured ash bats for a number of professional teams. Ash remained the wood species of choice until the late 1990s when maple bats were introduced to players, and a small number of players transitioned from ash to this new species of wood. In 2001, Barry Bonds broke the Major League Baseball (MLB) single-season home run record using maple bats. This feat caused the popularity of maple bats to increase dramatically as other players thought maple bats would magically increase their batting statistics.

As the popularity of maple bats increased, the rate at which bats were breaking into multiple pieces during games was perceived to have increased as well. In July 2008, experts in the scientific analysis of baseball, statistics, and the mechanical behavior of different wood species were appointed by MLB in cooperation with the MLB Players Association to examine the perceived bat durability issues and report findings to the MLB Safety and Health Advisory Committee at the end of the season. Over a 2½-month portion of the 2008 MLB season, 2232 bats were broken during game play, and 756 of these bats broke into multiple pieces [1]. Research showed that, among other factors, the slope-of-grain (SOG) of the wood played a major role in the likelihood of a bat breaking into multiple large fragments. The slope of grain of a wood describes the orientation of the wood grain with respect to the longitudinal centerline of the bat. Research also showed that while maple and ash bats were equally likely to break, maple bats were three times more prone to break into multiple pieces than ash bats.

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New manufacturing regulations with respect to (1) SOG and (2) changing the hitting surface for maple bats from edge grain to face grain were implemented after the 2008 season, and as a result, the rate of these multiple-piece failure (MPF) occurrences decreased by 30% [2]. After the 2009 season, additional regulations were implemented to restrict the species of wood that can be used to manufacture baseball bats, which reduced the amount of MPF occurrences by an additional 14% during the 2010 season [3]. All of the new regulations had the benefit that the improvements in bat durability came with changes that were fairly transparent to the players, i.e. there were no bat geometries or popular wood species that were prohibited from use.

Before the introduction of maple to the game in the 1990s, ash had been the wood of choice for over 100 years, and bat durability had not been a serious concern. To avoid any wood durability problems in the future should another new wood species be proposed for use in the game, Major League Baseball was interested in developing a scientific process for evaluating the durability and batted-ball performance of a new species of wood before it could be added to the list of approved species. Additionally, other species of wood with performance and durability characteristics similar to ash are being sought because of concerns that the emerald ash borer threatens to eradicate the ash forests from the United States within the next decade. If new species of wood are not introduced into Major League Baseball before ash is no longer available, then maple and the MPF risks associated with it may become even more prevalent than they are today. Northern white ash is taken to be the gold standard to which all other species will be compared for this proposed wood-certification methodology.

The scientific wood-evaluation process was proposed to be a combination of experimental and finite element methods. The experimental results are used to quantify the durability of a wood species relative to ash and to assist in the calibration of the wood material models used in the finite element analyses. The finite element analyses can be used to explore the relationship of the bat profile to durability and to determine the potential of a species to meet the durability criteria required for approval. The use of the finite element models reduces the number of wood bats that need to be used for the test phase of the evaluation. The finite element models also allow for case studies to be run, which can identify what bat properties positively or adversely affect bat durability.

This paper summarizes the finite element modeling that was used to investigate yellow birch baseball bats subject to ball impacts that induce SPFs (single piece failures) and MPFs. A single-piece failure of a wood baseball bat occurs when the bat cracks, but does not break into multiple large pieces. This type of failure is preferred over a multiple-piece failure because the bat remains intact, and no fragments of the bat leave the batter’s hands. Figure 1 shows an example of an SPF, for which a crack initiated but did not propagate fully across the diameter of the bat or fully down the length of the bat. A multiple-piece failure of a wood baseball bat occurs when the bat breaks into two or more large pieces. This type of failure is undesirable, as large and potentially sharp fragments can split from the bat and fly into the field or into spectator areas. MPFs typically require higher impact velocities to be induced than SPFs. Figure 2 shows an example of an MPF where a crack propagated down the length of the bat and almost entirely across the width of the bat along a diagonal line.

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Figure 1. An example of an SPF Figure 2. An example of an MPF

Note: Baseball is an American game where the dimensions of baseballs and bats are measured in inches and their weights are measured in ounces and batted-ball speeds are stated in mph. Thus, U.S standard units will be used throughout this paper as opposed to SI units—unless specified otherwise.

Experimental Program The apparatus used to conduct durability testing is the Automated Design Corporation (ADC) Bat Durability Testing System. This system is capable of firing baseballs at velocities up to 200 mph. In this testing apparatus, the bat is stationary prior to impact. A pair of ADC iBeam Screen Sensors and an ADC Velocigraph Speed Chronograph are used to measure the inbound velocity of the baseball by determining how long it takes the ball to travel through the 12-in. distance between the sensors. The sensors are accurate to within ±0.5 mph. The ADC machine is shown in Figure 3.

The baseball bat being tested is held stationary in the ADC machine by two pairs of roller grips constructed of two different rubber materials. The top set of rollers is made of a Tecamid Molybdenum Disulfide nylon material [4], and the rollers are clamped relatively tightly. The bottom set of rollers is made from a polyurethane material [5], and these rollers are loosely in contact with bat. This combination of rollers is intended to simulate a player’s grip. Bat durability tests using this setup have shown good correlation with bats broken in the field of play. Figure 3 and Figure 3b show images of the baseball bat sitting in the ADC machine and a close-up of the baseball bat sitting in the rollers, respectively.

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(a) (b)

Figure 3. ADC machine (a) with a baseball bat sitting in it and (b) with a close-up view of a baseball bat gripped by rollers

Finite Element Models

All finite element models (FEMs) used for this research were constructed using HyperMesh Version 11.0. FEMs of several popular bat models used by professional players were constructed. These bat models include cupped and uncupped versions of the C243, and uncupped models of the C271, I13, and C353. These FEMs were constructed using solid 8-noded brick elements containing a single Gauss point for analysis in LS-DYNA. The geometry of the four uncupped FEMs that were used for this research are shopwn in Figure 4, and the number of nodes and elements that comprise each bat FEM and the volume of each profile are summarized in Table 1.

Figure 4. C353, C271, C243, and I13 FEMs created for this research

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Table 1. Number of elements and nodes created in construction of bat models

Model Cup Elements Nodes Volume [in3] C243 Yes 156078 163132 82.197 C243 No 159984 179533 84.256 C271 No 130554 140540 76.812 C353 No 137430 145684 86.853 I13 No 127665 134604 84.957

Wood Material Model

The LS-DYNA Wood Material Model 143, which was developed for the Federal Highway Administration [6] was used as the basic material model. This material model allows for all essential material properties of wood to be implemented, e.g. MOE in the three principal directions for wood, density, MOR as a function of direction, and SoG (using AOPT). As used in this research, the slope-of-grain was assumed to be in one plane and uniform along the entire length of the bat. This material definition also has several other properties which can be input, e.g. to capture the strain-rate effects on the yield stress. However, these other options were left at the default values because their values as they apply to the woods considered in this current research were unknown when this research was performed.

In the constructed finite element model, a positive slope-of-grain is angled towards the surface impacted by the ball, whereas a negative slope-of-grain is angled towards the face opposite of the impact. This interpretation is shown visually in Figure 5.

Figure 5. Orientation of positive and negative slopes-of-grain in bat model

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Baseball FEM Construction

The baseball FEM that was used for this research was constructed for a currently ongoing MS thesis by Connolly [7]. The ball FEM construction involved correlating modeling and experimental results of a baseball impacting an aluminum baseball bat, and tuning the properties of the baseball so the modeling results of the baseball rebounding off the baseball bat correlated with the experimental velocities. These experimental and modeling bat-ball collisions occurred between 110-140 mph, which is roughly the same range that was being examined for the modeling performed in this study. The geometry of the ball model is a sphere of 1.4-in. radius, and consists of 12,096 solid elements and 12,589 nodes. The material prescribed to this ball FEM was LS-DYNA Material Type 6, which is a viscoelastic material.

ADC Fixture FEM Construction

The experimental dynamic durability testing of the bats are performed in the ADC Durability Testing System which supports bats between two sets of rubber rollers, and the two sets have different material properties. These rollers constitute the boundary conditions which support the bats in the ADC system. In the experimental system, the two sets of rollers have different material properties and are tightened differently. These rollers are mounted on an aluminum plate, which is free to rotate about a pivot point.

Failure Criterion

One of the most significant properties that must be implemented into the baseball bat model to capture the bat breakage is the material failure criterion. The MOR is a failure criterion that, when implemented, causes failure to occur when the effective stress induced by a bat-ball collision exceeds the prescribed MOR value in one or more directions. While MOR can be calculated from the dowel test data that is performed, preliminary models showed that implementing these MOR values does not allow for the bat models to break as observed during experimental bat durability testing. This lack of correlation between MOR from dowel testing and durability testing is likely due to the slower loading rate of the machine used to perform the dowel testing relative the very high impact velocities of the bat-ball collisions. Therefore, a strain-to-failure criterion was implemented into the models though the use of the Add Ersion material option in LS-DYNA, which resulted in excellent correlation between the models and the test. This strain-to-failure criterion specifies that if the maximum principle strain induced by a bat-ball collision exceeded a specified value, then failure will occur at the location where this set strain-to-failure value is exceeded.

Tuning of Strain-to-Failure through Correlation

The strain-to-failure of a species of wood was determined by implementing some strain-to-failure value into a baseball bat model then correlating modeling and experimental results. The strain-to-failure is also treated as dependent on the density of the wood being tested, as several other properties that define a species’ material strength are also dependent on wood density.

FEMs of tested baseball bats were constructed by implementing the measured SoG and calculated density, as well as the MOE and MOR values determined through dowel testing which are associated with the density of the bat tested. The baseball FEM is positioned to impact the bat model at the same impact location and impact velocity that induced failure of the tested bat. Strain-to-failure values are then implemented into the model to determine what strain value, to

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the nearest tenth of a percent, produces the best correlation between modeling and experimental results.

Results

While the dowel test data was valuable in quantifying the MOE as a function of density, the dowel testing was unable to be performed at strain rates that are comparable to those experienced by the wood during a bat/ball impact. Because wood is a viscoelastic material, the strain to failure can be a function of the strain rate. Thus, for this research, the strain-to-failure of a wood species had to be determined through correlating modeling and experimental results of bat/ball impacts. This approach ensured that the strain-to-failure was determined using test data that were collected at a strain rate in the order of magnitude associated with bat durability. The parameters of a tested baseball bat, including profile, density (and corresponding MOE and MOR values), and slope-of-grain, are all included in the finite element model. The speed of the ball in the models is prescribed to be the speed that induced failure in the associated experiment to which the model is to be correlated. Parametric studies were then run to explore different prescribed strain-to-failure values, and the results were visually compared with what was observed experimentally, i.e. initiation point and path of the crack. The strain-to-failure value that results in the best visual correlation is considered the strain-to-failure of the combination of the yellow birch and density that was analyzed.

Finite element models of tested yellow birch bats were constructed, and strain-to-failure values were prescribed to determine what strain-to-failure in the finite element model produced results that correlated well with the high-speed video of the durability test. The bats that were chosen to be modeled broke in a manner that was expected for the impacted location. For example, bats impacted at the 14-in. location typically experience crack initiation around 6 in. above where the impact occurs and on the surface opposite of the impacted surface. .

Strain-to-failure is dependent on wood density, so low-density (< 0.0225 lb/in3), medium-density (0.0225-0.0250 lb/in3) and high-density (> 0.0250 lb/in3) yellow birch bats were modeled to determine how the strain-to-failure changes with density. Models of impacts that occurred at the 14-in. location were created initially to determine what strains-to-failure were required for good modeling-experimental correlation. Figures 6 through 8 show comparisons of the model from the parametric study of varying the strain-to-failure that correlated best with the experimental results in that density class.

The results in Figures 6 through 8 show that the strain-to-failure for low- density yellow birch is 3.5%, increases to 4.6% for medium-density, and remains at 4.6% for high-density. Using these data, a plot was created to determine what strain-to-failure should be applied to a yellow birch model for any wood density. This plot is shown in Figure 9.

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14-in impact

Broke @ 147 mph Max vel. w/o break @ 134 mph

135 mph ef=3.5%

[no break]

140 mph ef=3.5%

145 mph ef=3.5%

Figure 6. Strain-to-failure that resulted in good correlation for impacting 0.0217 lb/in3 low-density yellow birch bat at 14-in. location [Bat ID 0711-045]

14-in impact


150 mph ef=4.6%

[no break]

155 mph ef=4.6%

Figure 7. Strain-to-failure that resulted in good correlation for impacting 0.0239 lb/in3 medium-density yellow birch bat at 14-in. location [Bat ID 1011-018]

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14-in impact


135 mph ef=4.6%

[no break]

140 mph ef=4.6%

Figure 8. Strain-to-failure that resulted in good correlation for impacting 0.0261 lb/in3 high-density yellow birch bat at 14-in. location [Bat ID 0711-025]

Figure 9. Yellow birch strain-to-failure as a function of density

It is important to note that the relationship between strain-to-failure and wood density of yellow birch that is shown in Figure 9 was obtained using a very limited amount of data. As experimental bat and dowel testing have shown, there can be significant variability in material properties among samples for a species of wood. The tested bats that were modeled were chosen because their properties appeared to be average for their density class. However, it is recommended that additional testing and modeling should be performed in the future to increase

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the number of data points that can then be used to develop a better understanding of the relationship between the strains-to-failure as a function of density for yellow birch. With a relationship between strain-to-failure and wood density determined for yellow birch, albeit based on a limited data set, models of experimental 16-in. impacts were generated to investigate the credibility and robustness of the strain-to-failure/density relationship. The strains-to-failure prescribed to each bat model were determined using the relationship shown in Figure 9, and the results of the models were compared to the experimental results. Modeling results of these 16-in. impacts are shown in Figures 10 through 12.

16-in Impact


130 mph ef=3.6%

115 mph ef=3.6%

Figure 10. Correlation of 0.0220 lb/in3 (low-density) yellow birch bat impacted at the 16-in. location with 3.6% strain-to-failure prescribed [Bat ID 0711-044]

Figure 10 shows that prescribing a strain-to-failure of 3.6% for a 0.0220 lb/in3 (low-density) model produces good correlation, although the bat model still experiences failure at an impact velocity lower than the maximum impact velocity that the bat endured without breaking. Figure 11 shows that a modeled bat of 0.0246 lb/in3 (medium-density) does not experience failure when impacted at the maximum test velocity for a strain-to-failure of 4.6% prescribed, like was observed experimentally. Figure 12 shows that a modeled bat of 0.0258 lb/in3 (high-density) does not experience failure at 125 mph with a prescribed strain-to-failure of 4.6%, but does experience MPF for an impact at 130 mph. The actual bat experienced SPF at 125 mph, and the failure that occurred was not significant because the crack did not propagate very far across the diameter of the bat, i.e. an impact at a slightly lower velocity may not have induced any sign of breakage. It is also plausible that if the impact occurred at 130 mph, then the bat would have experienced an MPF as shown in the modeling results. Therefore, while visual correlation between the finite element model and experimental results is not achieved for a 4.6% strain-to-failure, the modeling results show that the strain-to-failure of this 0.0258 lb/in3 (high-density) bat may still be a good approximation.

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16-in Impact

Impact shown occurred @ 144 mph Max impact vel. @ 148 mph Bat did not break during test

145 mph ef =4.6%

Figure 11. Correlation of 0.0246 lb/in3 (medium-density) yellow birch bat impacted at the 16-in. location with 4.6% strain-to-failure prescribed [Bat ID 0711-054]

16-in Impact

Bat broke @ 125 mph Max vel. w/o break @ 118 mph

120 mph ef=4.6%

[no break]

125 mph ef=4.6%

[no break]

130 mph ef=4.6%

Figure 12. Correlation of 0.0258 lb/in3 (high-density) yellow birch bat impacted at the16-in. location with 4.6% strain-to-failure prescribed [Bat ID 0711-023]

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Conclusions

Finite element modeling of yellow birch bats in LS-DYNA were used to develop a method for simulating bat durability. Mat 143 was used in conjunction with the Mat Add Erosion option where the maximum principal strain criterion was found to provide realistic failure modes when the failure strain varied as a function of wood density.

References

1. 2008 Interdisciplinary Team. 2008. Options for Reducing Multi-piece Bat Failures in the 2009 Season, Presented to the MLB/MLBPA Safety and Health Advisory Committee November 21, 2008. MLB Offices in New York, New York. Final Report.

2. 2009 Interdisciplinary Team. 2009. Options for Reducing Multi-piece Bat Failures in the 2010 Season, Presented to the MLB/MLBPA Safety and Health Advisory Committee November 6, 2009. MLB Offices in New York, New York. Final Report.

3. 2012 Interdisciplinary Team. 2012. Study to Develop a Protocol for Adopting New Wood Species for Listing in the Wooden Baseball Bat Supplier Regulations. Final Report.

4. "Tecamid MDS - Molybdenum Disulfide Filled (MDS) ." Laird Plastics. N.p., 09 APR 2013. Web. 13 May 2013.

5. "Polyurethane." McMaster-Carr. N.p.. Web. 05 APR 2013. <http://www.mcmaster.com/#standard-polyurethane-rods/=mqhffv>

6. Manual for LS-DYNA Wood Material Model 143. U.S. Department of Transportation Federal Highway Administration, AUG 2007

7. Connolly, Tim. Design of an Injected Molded Composite Baseball Bat. Future M.S. Thesis, University of Massachusetts-Lowell.

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ATV and MATV Techniques for BEM Acoustics in LS-DYNAÒ

Yun Huang, Zhe Cui

Livermore Software Technology Corporation 7374 Las Positas Road, Livermore CA 94551

Abstract This paper presents the new ATV (Acoustic Transfer Vector) and MATV (Modal Acoustic Transfer Vector) techniques for BEM acoustics in LS-DYNA, which were implemented recently. Acoustic Transfer Vector provides the transfer function between the normal nodal velocity on structural surface and the acoustic response at selected field points; Modal Acoustic Transfer Vector provides similar transfer function, but is based on the excitation from modal shape vibrations. ATV and MATV reveal the inherent properties of structures and acoustic volume, and can be used to predict radiated noise from vibrating structures when combined with vibration boundary conditions. Particularly they are useful for the acoustic analysis of structures subjected to multiple load cases. Some examples are given to illustrate the application of the ATV and MATV techniques. For ATV, post-processing of the results in the form of binary plot database is also presented.

Introduction

Recently a bunch of acoustic boundary element methods (BEM) have been implemented to LS-DYNA [1]. These acoustic BEM can be used to predict the noise from a vibrating structure. They have wide application in auto NVH analysis, and other vibro-acoustic analysis.

To facilitate the acoustic analysis for the situation where multiple load cases are present, two new techniques ATV (Acoustic Transfer Vector) and MATV (Modal Acoustic Transfer Vector) have been implemented to the acoustic BEM.

ATV is defined as the transfer function between the normal nodal (elemental) velocity and the acoustic pressure at field points. Once all the ATV are obtained, the total acoustic pressure at field points can be computed by simple matrix – vector multiplication, as in equation (1)

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or equation (2) in short form

{ } [ ] { }nnmm vATVP ´= (2)

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In equation (1), ip is the acoustic pressure at field point i and jv is the actual normal velocity at node j. m is the number of field points and n is the number of nodes in boundary elements. ji,W represents the acoustic pressure at field point i, due to unit normal velocity at node j. Please note that all the variables in equations (1) and (2) are dependent on frequency w=2p f. Besides, the variables in both equations are complex. As indicated by equation (2), for a given frequency and given geometry, the ATV matrix is constant and is not dependent on the loading condition. Once the ATV matrix is obtained, for any given normal velocity vector { }nv , a simple matrix-vector multiplication can provide the total pressure { }mP quickly. That is why this method is very efficient and provides huge saving in CPU times if multiple load cases have to be considered.

To get the velocity vector { }nv , one can run lab testing, road testing, or numerical vibration analysis such like using the keyword *FREQUCNY_DOMAIN_SSD in LS-DYNA. The *FREQUCNY_DOMAIN_SSD keyword provides the solution for harmonic steady state vibration based on mode superposition method. For each vibration frequency, the structural response is composed of contribution from all the involved eigen modes. This suggests that one can first run acoustic computation for each eigen mode, to get acoustic contribution from each mode, and then do a modal superposition to get the total acoustic pressure, using the same modal coordinates obtained in SSD calculation. This brings us to the concept of modal ATV, or MATV, as illustrated by equation (3)

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Or equation (4) in short form

{ } [ ] { }llmm qMATVP ´= (4)

Where, ji,Y represents the acoustic pressure at field point i, due to the normal velocity boundary condition for eigen mode j. Once again ip is the acoustic pressure at field point i. jq is the modal coordinates for mode j. jq is obtained from SSD (Steady State Dynamics) analysis. m is the number of field points and l is the number of modes involved in the mode superposition procedure. Once again all the variables in equation (1) are dependent on frequency w=2p f and they are all complex. Please note that ATV and MATV can be related by the following equation

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Where i is the imaginary unit ( 1-=i ) and { }nu is the displacement vector. The matrix [ ] ln´f is the modal shape matrix, provided by implicit eigenvalue analysis. { }lq is the modal coordinate vector.

One can see, for each load case, only the modal coordinates vector { }lq need to be updated and once it is ready, a simple matrix-vector multiplication can be performed and it provides the solution for acoustic pressure vector at the field points.

For a real practical problem, the number of eigen modes involved is usually much less than the number of nodes in the boundary elements ( ln << ), so the MATV approach represented by equation (3) or (4) is more efficient than the ATV approach, if the vibration simulation can be accomplished by SSD.

For ATV, a binary plot database d3atv is provided in LS-DYNA, to visualize the acoustic pressure due to unit normal velocity at each surface node. This helps to study the contribution to acoustic pressure from each surface node. To get d3atv database, the keyword *DATABASE_FREQUENCY_BINARY_D3ATV is needed in LS-DYNA keyword input deck. For more details about this keyword, please refer to LS-DYNA Keyword Users’ Manual [2].

Several examples are given below to demonstrate the ATV and MATV capabilities.

ATV for a simplified engine model

Figure 1 shows a simplified engine model and the location of two field points. To run ATV analysis for this model, the keyword *FREQUENCY_DOMAIN_ACOUSTIC_BEM_{ATV} is employed. In this keyword, we set up the range of frequencies to compute, the number of excitation frequencies, the location of field points, and some other parameters for BEM Acoustic analysis. More details about this keyword can be found in reference [2].

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Field point 2Field point 1

Figure 1: A simplified engine model for ATV computation

In LS-DYNA computation, we run BEM analysis for unit normal velocity from each of the surface nodes, and compute the acoustic pressure at the two field points. Please note that for each frequency, one does not need to reform the complex influence matrix for each surface node under consideration --- it is formed only once. We only need to update the R.H.S. of the equation system (see equation (6) below).

( )[ ] ( ){ } ( ){ }www yxC = (6)

The results of the ATV computation are given in 1) ASCII files

ATV_FIELD_PT_ID ATV_DB_FIELD_PT_ID And 2) BINARY database d3atv.

In ATV_FIELD_PT_ID, the complex pressure for one field point (indicated by ID) for user specified excitation frequencies is given for each surface node. When multiple field points are present, LS-DYNA will generate multiple ATV_FIELD_PT_ID, with different ID.

In ATV_DB_FIELD_PT_ID, the SPL (Sound Pressure Level, or dB) for the field point ID for user specified excitation frequencies is given for each surface node.

D3atv is a binary plot database, and it is written in the same format as d3plot and other binary plot databases in LS-DYNA. It is accessible to LS-PrePostÒ. It shows the real part, imaginary part and dB values of the acoustic pressure, at each field point, at each frequency, due to unit normal velocity at each surface node. For this example, some of the results are given in Figure 2,

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Figure 2: Real part of pressure ATV at field point 1

and Figure 3.

Figure 3: Imaginary part of pressure ATV at point 2

From d3atv, such as Figures 2 and 3, people can see easily that which part of the surface gives more contribution to the final acoustic pressure at field points.

MATV for a simplified engine model

Figure 4 shows a simplified door model. It is fixed at the upper edge and the 4 holes near the lower edge. It is subjected to 10 load cases. For each of the load case, a nodal force spectrum is given at one node on the door. The range of frequency is same for the 10 load cases. So this provides a good example for using the MATV technique in LS-DYNA.

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Figure 4: A door model for MATV computation

To using the MATV technique, the first thing to do is to generate the MATV matrices. The excitation frequency is 100-500 Hz, with 101 equally spaced frequencies. So for running implicit eigenvalue analysis, modes up to 600 Hz (which is 20% higher than the highest excitation frequency) is needed. Keyword *FREQUENCY_DOMAIN_ACOUSTIC_BEM_{MATV} is used, without specifying any loading or excitation conditions for acoustic computation. Keywords *CONTROL_IMPLICIT_GENERAL, *CONTROL_IMPLICIT_EIGENVALUE are set, to perform the implicit eigenvalue analysis, and generate d3eigv binary plot database. LS-DYNA will extract the eigen vectors { }jf from d3eigv. For each excitation frequency f, LS-DYNA will generate the psedo-velocity boundary condition { }ji fw ( fpw 2= ) and run BEM acoustic computation to get the MATV matrix.

For the second step, the keyword *FREQUENCY_DOMAIN_SSD is adopted, to run steady state dynamic computation for given nodal force loading. SSD will generate the modal coordinates { }lq for each excitation frequency. The keyword *FREQUENCY_DOMAIN_ACOUSTIC_BEM_{MATV} is also needed and we set IREST=1, which means that we are running restart BEM acoustic computation based on existing MATV.

To check the accuracy of the method, we run this problem also in the traditional way (SSD + BEM Acoustic computation) without using MATV. The results for one load case by the two different methods are plotted in Figure 5, and one can see that the two curves match very well.

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Figure 5: SPL at field point

The total CPU time for running 1 load case and 10 load cases is listed in Table 1. The computation is performed on Intel Xeron CPU E5504 @2.00 GHz (CPU MHz: 1596.00 cache size 4096 KB). Three different methods are used: 1) Direct SSD + traditional BEM, which means that we go through the whole procedures (Modal analysis, SSD and tradition BEM) for each load case; 2) Restart SSD + traditional BEM, which means that starting from the 2nd load case, we skip the modal analysis part, and run a restart SSD using existing d3eigv, and then the traditional BEM; and 3) Restart SSD + MATV BEM, which means that we skip the modal analysis part starting from the 2nd load case, and run a restart SSD and then use the MATV based BEM to get the acoustic pressure for all the load cases.

For 1) Direct SSD + traditional BEM method, the total CPU time for 10 load cases is simply 10 times of the CPU time for one load case. For 2) Restart SSD + traditional BEM, starting from the 2nd load case, LS-DYNA can make use of the existing d3eigv database, and run modal superposition to get SSD response directly. This way we can skip the time-consuming modal analysis step, and gain some CPU saving. The most CPU saving is observed in 3) Restart SSD + MATV BEM. For 3), the step 1 (generating the MATV matrices) is needed only once and the step2 (BEM acoustic calculation based on MATV) is repeated 10 times if 10 load cases are present. Since the CPU time for step 2 is so small one can expect that when more load cases are present, more CPU saving can be achieved by the MATV BEM, comparing to the traditional BEM.

Cases 1) Direct SSD + traditional BEM

2) Restart SSD + traditional BEM

3) Restart SSD + MATV BEM

1 load case 2 h 39 m 50 s 2 h 39 m 50 s 4 h 40 m 56 s

10 load cases 26 h 38 m 18 s 25 h 53 m 13 s 4 h 41 m 10 s

Table 1: CPU time for different methods (h: hour; m: minute; s: second)

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For the “1 load case”, one always has to start from modal analysis and generate d3eigv binary database. So the CPU time for methods 1) and method 2) is same for the “1 load case”. Method 3) takes longer time to run for the “1 load case” but the extra time is well compensated by the huge saving in computation for additional load cases.

Conclusion

For BEM Acoustic solver in LS-DYNA, ATV and MATV techniques have been implemented. ATV provides the transfer function between the normal nodal velocity on structural surface and the acoustic response at selected field points; Modal Acoustic Transfer Vector provides similar transfer function, but is based on the excitation from modal shape vibrations. ATV and MATV are properties of the structure and they are not dependent on the loading conditions. Once computed, they can be used for many load cases. That is why they are useful and provide efficient tools when one needs to run acoustic computation for multiple load cases.

Another possible application of ATV and MATV is the inverse acoustic analysis. Based on the measured acoustic environment, and using the ATV / MATV techniques, one is able to locate the source of vibration excitation. This can be useful to solve the auto BSR (Buzz, Squeak and Rattle) problems.

References 1. Huang Y., Souli M., Development of acoustic and vibro acoustic solvers in LS-DYNA®. Proceedings of

the 10th International LS-DYNA® Users’ Conference, June 8-10, 2008, Dearborn, Michigan.

2. LS-DYNA Keyword User's Manual, Livermore Software Technology Corporation, January 14, 2014 (revision: 4571).

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