ARL-TR-7927 ● JAN 2017

US Army Research Laboratory

Polymeric Materials Models in the Warrior 

Injury Assessment Manikin (WIAMan)

Anthropomorphic Test Device (ATD) Tech 

Demonstrator

by M Chowdhury, D Crawford, M Shanaman, M Boyle, 

R Armiger, C Bell, K Lister, and A Shirley

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ARL-TR-7927 ● JAN 2017

US Army Research Laboratory

Polymeric Materials Models in the Warrior 

Injury Assessment Manikin (WIAMan)

Anthropomorphic Test Device (ATD) Tech 

Demonstrator

by M Chowdhury and D Crawford

Weapons and Materials Research Directorate, ARL

M Shanaman, M Boyle, and R Armiger

Johns Hopkins Applied Physics Lab, Laurel, MD

C Bell, K Lister, and A Shirley

Corvid Technologies, Mooresville, NC

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1. REPORT DATE (DD-MM-YYYY)

January 2017

2. REPORT TYPE

Technical Report

3. DATES COVERED (From - To)

06/2015 to 09/2016

4. TITLE AND SUBTITLE

Polymeric Materials Models in the Warrior Injury Assessment Manikin 

(WIAMan) Anthropomorphic Test Device (ATD) Tech Demonstrator

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

M Chowdhury, D Crawford, M Shanaman, M Boyle, R Armiger, C Bell, 

K Lister, and A Shirley

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

US Army Research Laboratory

ATTN: RDRL-DPW

Aberdeen Proving Ground, MD 21005

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ARL-TR-7927

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12. DISTRIBUTION/AVAILABILITY STATEMENT

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The Warrior Injury Assessment Manikin (WIAMan) Engineering Office has been developing a biofidelic anthropomorphic 

test device (ATD) to enable the live-fire test and evaluation community to address the deficiencies associated with the use of 

the Hybrid III ATD to assess the risk of mounted-Soldier injuries subjected to under-body blast. A finite-element (FE) virtual 

modeling tool has been developed to support the design and development of the WIAMan ATD. Material characterization is 

one of the critical challenges facing the ATD modeling community because of the lack of adequate material models and 

inconsistency between material models available in different FE codes. The WIAMan modeling and simulation team 

systematically characterized the material properties using experimental data for 8 polymeric materials used in key components 

in the WIAMan ATD Tech Demonstrator. Two modeling teams independently simulated the WIAMan ATD in vertical 

accelerative loading simulations using 2 different modeling platforms (LS-DYNA and Velodyne). The approaches to derive 

the material parameters, constitutive material models, and the fitting algorithms are discussed in this report. A brief summary 

of the whole-body simulation results of an ATD response due to vertical accelerative loading is provided and compared to 

illustrate the predictive capability of the derived material models. 

15. SUBJECT TERMS

under-body blast, finite-element model, Warrior Injury Assessment Manikin, WIAMan ATD, anthropomorphic test device,

validation

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M Chowdhury

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(301) 394-2917

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Contents

List of Figures v

List of Tables vii

1. Introduction 1

2. WIAMan Material Description and Material Test Data 4

2.1 WIAMan Material Description 4

2.2 WIAMan Material Test Data 4

3. Velodyne Material Models 6

3.1 Parameterization Procedure 7

3.2 Results for Velodyne Materials Models 14

3.2.1 Proflex 30 Pelvis Flesh 15

3.2.2 XE1031 Foot Flesh 16

3.2.3 FD70 Foot Plate 17

3.2.4 Delrin Calcaneus Cap 18

3.2.5 E1030AL Flesh (Other) 19

3.2.6 Butyl Rubber (75 Shore A) Compliant Elements 20

3.2.7 Rencast 6425 Tailbone 21

3.2.8 TC892 Pelvis Bone 22

4. LS-DYNA Material Models 23

4.1 Polymer Material Models 24

4.1.1 *MAT_OGDEN_RUBBER 24

4.1.2 *MAT_BERGSTROM_BOYCE_RUBBER 25

4.1.3 *MAT_SIMPLIFIED_JOHNSON_COOK 26

4.1.4 *MAT_BLATZ-KO_RUBBER 27

4.2 Polymer Fitting Procedure 27

4.2.1 MCalibration Software 30

4.2.2 LS-OPT Software 31

4.2.3 Molded Neck Rubber Fit Procedure 31

4.3 Polymer Fitting Results 32
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4.3.1 Butyl Rubber 75 Shore A Compliant Elements and Spine 

Rubber 32

4.3.2 Proflex 30 Polyurethane Pelvis Flesh 33

4.3.3 E1030AL Polyurethane Arm, Leg, and Abdomen Flesh 34

4.3.4 XE1031 Polyurethane Foot Flesh 35

4.3.5 FD70 Polyurethane Foot Plate 36

4.3.6 Delrin Calcaneus Cap 37

4.3.7 TC892 Polyurethane Pelvic Bone 38

4.3.8 Rencast 6425 Polyurethane Tailbone 39

4.3.9 ISODAMP Heel Plug 40

5. Typical WIAMan Strain Rate Environment 41

6. Whole-Body ATD Model Simulation Results 44

7. Conclusions 50

8. References 52

List of Symbols, Abbreviations, and Acronyms 55

Distribution List 56
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v

List of Figures

Fig. 1 Manikin FEM development timelines: historical perspective ...............2

Fig. 2 WIAMan ATD TD polymeric material definition.................................4

Fig. 3 Veryst stress-strain results at 0.1/s strain rate........................................8

Fig. 4 The Veryst Proflex 30 compression material test specimen (left) and 

the FE mesh counterpart (right).............................................................8

Fig. 5 Velodyne schematic for the Veryst compression testing.......................9

Fig. 6 Process flow for inverse analysis using DAKOTA to iterate parallel runs 

of Velodyne ..........................................................................................12

Fig. 7 Comparison of the Ogden viscoelastic model to experimental 

compression data for the Proflex 30 pelvis flesh.................................15

Fig. 8 Comparison of the Ogden viscoelastic model to experimental 

compression data for the XE1031 foot flesh........................................16

Fig. 9 Comparison of the Ogden viscoelastic model to experimental 

compression data for the FD70 foot plate............................................17

Fig. 10 Comparison of the Ogden viscoelastic model to experimental 

compression data for the Delrin calcaneus cap....................................18

Fig. 11 Comparison of the Ogden viscoelastic model to experimental 

compression data for the E1030AL flesh.............................................19

Fig. 12 Comparison of the Ogden viscoelastic model to experimental 

compression data for the butyl rubber 75A..........................................20

Fig. 13 Comparison of the Ogden viscoelastic model to experimental 

compression data for the Rencast 6425 tailbone..................................21

Fig. 14 Comparison of the Ogden viscoelastic model to experimental 

compression data for the TC892 pelvis bone.......................................22

Fig. 15 BB fit for butyl rubber (top) vs. Ogden+Prony fit (bottom) at strain 

rates of 1 s–1 (red) and 50 s–1 (green)...................................................28

Fig. 16 Performance results of the tibia and calcaneus load cells during SoD 

and WH1a load cases using different foot flesh material models........29

Fig. 17 Butyl rubber 75 Shore A material fit ...................................................33

Fig. 18 Pelvis flesh material fit ........................................................................34

Fig. 19 Arm, leg, and abdomen flesh material fit ............................................35

Fig. 20 Foot flesh material fit...........................................................................36

Fig. 21 Foot plate material fit...........................................................................37

Fig. 22 Calcaneus cap material fit....................................................................38

Fig. 23 Pelvis bone material fit ........................................................................39

Fig. 24 Tailbone material fit.............................................................................40
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vi

Fig. 25 Heel plug material fit ...........................................................................41

Fig. 26 Strain rates experienced by soft polymers during the VALTS test at 

WH1a levels (4 m/s at a 5-ms TTP floor, and seat, no PPE)..............42

Fig. 27 Strain rates experienced by soft polymers during the VALTS test at 

WH2a levels (6 m/s at a 5-ms TTP floor, 4 m/s at a 10-ms TTP seat, 

no PPE) ................................................................................................43

Fig. 28 Strain rates experienced by soft polymers during the VALTS test at 

WH2b levels (6 m/s at a 5-ms TTP floor, 4 m/s at a 10-ms TTP seat, 

with PPE).............................................................................................43

Fig. 29 Velocity history from the WH1A and WH2A VALTS tests that are 

employed as the simulation boundary conditions................................45

Fig. 30 Match pair validation results for the lower extremity at the heel and 

mid-tibia sensor regions for the simulation and the experiment under 

the WH1a test condition.......................................................................46

Fig. 31 Match pair validation results for the lower and upper neck sensor 

regions for the simulation and the experiment under the WH1a test 

condition ..............................................................................................46

Fig. 32 Match pair validation results for the lower extremity at the femur and 

tailbone sensor regions for the simulation and the experiment under the 

WH1a test condition ............................................................................47

Fig. 33 Example cross-plots of the Velodyne simulation and test for WH1A 

(neck calcaneus and tibia)....................................................................48

Fig. 34 Example cross-plots of the Velodyne simulation and test for WH1A 

(femur and tailbone).............................................................................49
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vii

List of Tables

Table 1 Veryst engineering materials tests analyses summary...........................6

Table 2 Veryst material tests...............................................................................7

Table 3 Hyperelastic fit parameters for the Proflex 30 pelvis flesh..................15

Table 4 Viscous fit parameters for the Proflex 30 pelvis flesh.........................15

Table 5 Hyperelastic fit parameters for the XE1031 foot flesh ........................16

Table 6 Viscous fit parameters for the XE1031 foot flesh ...............................16

Table 7 Hyperelastic fit parameters for the FD70 foot plate ............................17

Table 8 Viscous fit parameters for the FD70 foot plate....................................17

Table 9 Hyperelastic fit parameters for the Delrin calcaneus cap ....................18

Table 10 Viscous fit parameters for the Delrin calcaneus cap............................18

Table 11 Hyperelastic fit parameters for the E1030AL flesh .............................19

Table 12 Viscous fit parameters for the E1030AL flesh ....................................19

Table 13 Hyperelastic fit parameters for the butyl rubber 75A..........................20

Table 14 Viscous fit parameters for the butyl rubber 75A .................................20

Table 15 Hyperelastic fit parameters for the Rencast 6425 tailbone ..................21

Table 16 Viscous fit parameters for the Rencast 6425 tailbone .........................21

Table 17 Hyperelastic fit parameters for the TC892 pelvis bone .......................22

Table 18 Viscous fit parameters for the TC892 pelvis bone...............................22

Table 19 WIAMan LS-DYNA polymer materials..............................................23

Table 20 Blatz-Ko fit parameters for select WIAMan polymers........................32

Table 21 Butyl rubber 75 Shore A material parameters .....................................32

Table 22 Pelvis flesh material parameters ..........................................................33

Table 23 Arm, leg, and abdomen flesh material parameters ..............................34

Table 24 Foot flesh material parameters.............................................................35

Table 25 Foot plate material parameters.............................................................36

Table 26 Calcaneus cap material parameters......................................................37

Table 27 Pelvis bone material parameters ..........................................................38

Table 28 Tailbone material parameters...............................................................39

Table 29 Heel plug material parameters.............................................................40

Table 30 CORA summary table for the WIAMan TD WH1A Velodyne 

simulations...........................................................................................50
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viii

INTENTIONALLY LEFT BLANK.
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1

1. Introduction

Historically, the live-fire test and evaluation (LFT&E) community has employed

Hybrid III physical manikins for vehicle survivability and occupant safety 

assessment.

1 The Near-Term Under-Body Blast (N-T UBB) and Under-Body Blast 

(UBB) Methodology programs are also using a Hybrid III anthropomorphic test 

device (ATD) analytical model to analyze and understand the effects of blasts on 

vehicles.

2 The Hybrid III analytical model currently used by military vehicle 

analysts has been continuously updated to address the model’s inherent deficiencies 

and make the simulated model’s behavior more compatible for measuring occupant 

responses in a vertical accelerative loads associated with UBB.

2 The Hybrid III, in 

its best form (originally intended for automotive crash safety), is inadequate, has 

usability issues, and lacks the biofidelity to determine the risk of vehicle-mounted 

occupant injury in an UBB environment.

2–4 The Warrior Injury Assessment 

Manikin (WIAMan) Engineering Office (EO), sponsored by the Director, 

Operational Test and Evaluation (DOT&E), and executed by the Army, has been 

developing a biofidelic ATD to enable the LFT&E community to address the 

deficiencies associated with the use of the Hybrid III ATD and assess the injury 

risk to mounted Soldiers subjected to UBB.

5

The WIAMan EO, positively encouraged by the ATD modeling community 

recommendations,2,4 initiated a modeling and simulation (M&S) effort to develop 

an analytical tool to predict the response of the ATD to vertical accelerative 

loading. The analytical finite-element model (FEM) provided a virtual tool for the 

WIAMan EO to support ongoing ATD design development iterations to achieve 

strength-of-design, biofidelity, and usability requirements.

6,7 A general overview 

of the FEM development methods is available in the literature.

8,9 System-level 

whole-body model validation was based on paired experimental tests run on the

Johns Hopkins University Applied Physics Laboratory (JHU-APL) Vertically 

Accelerated Load Transfer System (VALTS). The VALTS is a vertical impact 

simulator that allows laboratory test simulation of vertical accelerative loading of 

various UBB loading profiles and scenarios.

10 Two independent solver platforms 

(LS-DYNA and Velodyne) have been employed in parallel across 2 teams to model 

the WIAMan ATD. Combined, these 2 FEMs provided an opportunity to cross 

check predictability and complement weakest link, thus increasing confidence in 

the models’ predictive capability. A competitive environment dominated the entire 

model development phase that drove the modelers to expedite the whole-body 

model development process at an unprecedented rate (see the historical perspective 

presented in Fig. 1). 
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Fig. 1 Manikin FEM development timelines: historical perspective

The WIAMan M&S team was commissioned in August 2014 and, in a relatively 

short 18-month period, a functional and validated FEM of the Tech Demonstrator 

(TD) was developed to support the design development of the ATD. The WIAMan 

M&S team has been supporting the Generation (Gen) 1 (and anticipates to support 

Gen 2) phase of the ATD development and they are planning to produce a validated 

and verified (V&V) FEM of the production WIAMan ATD in a relatively shorter 

time period than many other manikin development timelines (see Fig 1). Rapid 

progress in the WIAMan ATD model development cycle was essential to inform a 

demanding, ongoing ATD design effort, particularly during the critical design 

development phase. Additionally, WIAMan EO’s farsightedness in characterizing 

various ATD polymeric materials early in the project cycle contributed immensely 

in the model development process. 

The success of an FEM depends primarily upon the model’s ability to predict the 

necessary physics and interactions of the simulated environment. A simulated 

environment can be summed up in 3 categories: 1) initial conditions (ATD posture 

and rig setup), 2) boundary conditions (input velocity and rig constraints like belts), 

and 3) mechanical system consisting of materials and mechanism (geometry). For 

example, in vertical acceleration testing of a seated manikin within the VALTS 

environment, the vertical impactor that drives the seated ATD provides the input to 

the ATD, the supporting mechanisms that restrain the ATD are the boundary 

conditions, and the ATD itself is the mechanical system. A proper representation 

of the initial conditions, the input force that drives the simulated environment, the 

boundary conditions that define how the system is driven or acted upon by external 
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3

means (forces), and the material systems and mechanisms that constitute the model 

are the primary factors that govern a model’s predictive capability. Among the 3

factors, material characterization is the single most critical challenge facing the 

ATD modeling community because of the lack of adequate material models and 

inconsistency among material models available in different FE codes.

4,11 The 

WIAMan M&S effort arguably addressed these 2 critical ATD modeling challenges 

in its undertakings. The WIAMan M&S used experimentally derived material data 

to construct material models, and 2 modeling teams independently simulated the 

WIAMan ATD vertical accelerative loaded simulations in 2 different platforms 

(LS-DYNA and Velodyne). The other 2 factors affecting the accuracy of 

simulations are more or less manageable, since the input to the model is generally 

deterministic and the initial as well as boundary conditions can be verified in a 

controlled test environment. 

This report documents the material characterization process to extract material 

model parameters specific to the 2 FEM codes (LS-DYNA and Velodyne) for 8

polymeric materials used in key components in the WIAMan ATD TD. There are 

multiple constitutive models in each of the FEM codes used in this effort. LSDYNA has a variety of material models that can model polymeric materials 

behavior using an empirical or rational approach.

12‒14 Velodyne has their own 

material models, mostly inclusive of those available in the LS-DYNA code. The 

constitutive material models that these 2 codes used in their numerical simulations 

were derived from the same experimental data. Thus, the inconsistency between the 

material models used by 2 different codes is of little concern, since the simulation 

results were compared and verified against the same set of test data with a common 

reference threshold. The use of 2 FEM codes in solving an identical simulation 

environment also provided an opportunity to test the hypothesis that vertical 

accelerative response simulation of an ATD is independent of solver types given 

that the material models are derived from the same source. The approaches to derive 

the material parameters, the constitutive materials models, and the fitting 

algorithms are discussed in the report. This report also presents the respective 

model parameters for both models. Finally, the whole-body simulation results of 

both models of an ATD response due to vertical accelerative loading are compared 

using identical experimental data to document the predictive capability of the 

material models. 
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2. WIAMan Material Description and Material Test Data

2.1 WIAMan Material Description

The WIAMan TD consists of metallic structural components, specifically 

aluminum, steel, brass, tungsten, and titanium alloys, as well as complex 

hyperelastic and rate-dependent polymers, elastomers, and others. The latter of 

these two material classes dictates the compliance of the WIAMan and generally 

feature strain-rate dependent properties and thus the load responses and kinematics 

of the system are often governed by them. For this reason, it is important to 

accurately capture the behavior of these materials with regard to both ratedependence and the stress-strain relationship. A list of representative commercially 

available polymeric materials, along with their basic material property definitions, 

currently used within the WIAMan components are shown in Fig. 2. 

Comprehensive material property descriptions for the WIAMan TD polymers are 

documented by Crawford et al.

15

Fig. 2 WIAMan ATD TD polymeric material definition

2.2 WIAMan Material Test Data

Proper characterization of materials is vital to the success of an FE simulation. No

simulation can serve its purpose unless the material behavior is correctly simulated. 

Material tests are needed to extract its behavior in different simulated environment 

such as tension, compression, loading, and unloading conditions. Particularly the 

material test data for high-strain-rate effects are important for the accelerative 
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5

vertical loading environment for which the WIAMan ATD has been designed.

4 An 

extensive materials testing program to extract material characteristics data for 

polymeric materials had been executed to support the WIAMan model 

development. Veryst Engineering LLC (Needham Heights, MA; www.veryst.com), 

a leading testing lab for characterization of complex nonlinear viscoelastic 

materials, performed the dynamic material tests for the WIAMan TD materials. 

Veryst Engineering designed custom test methods to capture the nonlinear, strainrate-dependent response of the materials characterized. The specific details of each 

customized test and the material test results are described in the literature by 

Crawford et al.

15 The test results provide a comprehensive assessment of the 

material performance in tension and compression over a broad range of engineering 

strain rates given. 

Material characterization tests include the following:

• Monotonic uniaxial tension tests (≅0.01 s–1, 0.10 s–1, 1.0 s

–1 engineering 

strain rate) 

• Monotonic uniaxial compression tests (≅0.01 s–1, 0.10 s–1, 1.0 s–1

engineering strain rate) 

• The cyclic uniaxial tension tests (0.0033 s

–1

, 0.033 s–1, 0.33 s–1 engineering 

strain rate) 

• The cyclic uniaxial compression tests (0.01 s–1, 0.10 s–1, 1.0 s

–1 engineering 

strain rate) 

• High rate drop tower – tension (30 and 400 s–1) 

• High rate drop tower – compression (≅50 and 150 s–1) 

• Split Hopkinson pressure bar (SHPB) – compression (≅500 and 1000 s–1) 

• Bulk modulus, room temperature (≅0.01 s–1) 

• Failure test (≅0.01 s–1), wwheeeeee, ss−1 ii pp ss ssssssss 1

ssssssssssss

The Veryst test result summary of mechanical response behavior of the tested

materials is presented in Table 1.
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Table 1 Veryst engineering materials tests analyses summary

Material 

type

Trade 

name

Location in 

WIAMan

Dominant material 

behavior

Recommended material 

model

Polyurethane Proflex 30 Pelvis flesh A nonlinear viscoelastic 

response with strainrate effect

Both a simple hyperelastic 

or a more accurate 

nonlinear viscoelastic 

material model

Polyurethane XE1031 Foot flesh A nonlinear viscoelastic 

response with strainrate effect

A nonlinear viscoelastic

Polyurethane FD70 Foot plate A nonlinear viscoelastic 

response with strainrate effect

A nonlinear viscoelastic

Acetal resin Delrin Calcaneus cap A nonlinear viscoelastic 

response with strainrate effect

A nonlinear viscoelastic

Polyurethane E1030AL Flesh-other A nonlinear viscoelastic 

response with a little 

strain-rate effect

A nonlinear viscoelastic

Butyl rubber 75 Shore A 

(Custom)

Leg and 

spine compliant 

elements

A nonlinear viscoelastic 

response with a strong 

strain-rate effect

A nonlinear viscoelastic

Polyurethane Rencast 

6425

Tailbone A nonlinear viscoelastic 

response with a strong 

strain-rate effect

A nonlinear viscoelastic

Polyurethane TC892 Pelvic bone A nonlinear viscoelastic 

response with a little 

strain-rate effect

A nonlinear viscoelastic

Based on the material test data, nonlinear viscoelastic and viscoplastic multirate 

material models were fit to the experimental data to develop the constitutive 

material models by both M&S teams. Final selection of the material model 

approach was determined based on 1) the best fit to the stress-strain curves for each 

material and 2) stability of the material over the variety of applied loading 

conditions. Two different approaches to material characterization used by 2

independent M&S teams are described next.

3. Velodyne Material Models

The following sections describe the material constitutive models used in the 

WIAMan Velodyne model, which relate an element’s deformation to the resulting 

internal stress state. The materials models in the Velodyne ATD model are all in 

agreement with the recommended material models suggested by Veryst 

Engineering (see Table 1). 
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3.1 Parameterization Procedure

The following 8 polymeric materials in Table 2 were tested and characterized by 

Veryst Engineering. These materials were selected for testing as there were no 

available large-strain, high-strain-rate characterization data of the materials chosen 

for the WIAMan TD. Also, these materials are very compliant relative to the 

metallic structural components and thus strongly influence the WIAMan ATD 

response compared to the metals as quantified by the load cells and accelerometers 

responses due to vertical accelerative loading. 

Table 2 Veryst material tests

Material type Trade name

Location in 

WIAMan Velodyne model

Polyurethane Proflex 30 Pelvis flesh proflex30_ogv

Polyurethane XE1031 Foot flesh Foot_Flesh_Fit3

Polyurethane FD70 Foot plate Foot_Plate_ogv

Acetal resin Delrin Calcaneus cap Calcaneus_Cap_ogv

Polyurethane E1030AL Flesh-other flesh_og_visco

Butyl rubber 75 Shore A 

(Custom)

Compliant elements Veryst_BR75A_og_visco

Polyurethane Rencast 6425 Tailbone rencast_ogv

Polyurethane TC892 Pelvic bone tc892_OGV

For each of the materials shown in Table 2, Veryst performed a variety of material 

characterization tests at different strain rates. Measured forces and displacements

(using digital image correlation for tensile testing and fiducial marker tracking for 

compression) were extracted from the experimental data and converted into the true 

stress–true strain plots summarized in Fig. 3. The low-speed compression tests were 

performed with an MTS rig up to a strain rate of 1.0 s–1, and the higher-strain-rate 

compression tests were performed in a drop rig. Additional detail on the Veryst 

testing methodolgy and results can be found in the material characterization reports 

available through the WIAMan EO.

15
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Fig. 3 Veryst stress-strain results at 0.1/s strain rate

The stress-strain data provided the basis for the Corvid material model fitting 

procedure. The quasistatic and high-rate compression test data were used 

exclusively for the fitting procedure with the understanding that most of these 

materials would be predominately loaded in compression within the WIAMan. 

Note that this approach then assumes that the tensile response is approximately 

equivalent to the compressive response. Each of the compressive material test cases 

was replicated in Velodyne using the actual geometry of the specific test specimen. 

An example of the Proflex 30 pelvis flesh compression material test specimen as 

compared to the computational specimen is depicted in Fig. 4. The test specimen in 

this case was meshed with 4,620 solid hexahedral single integration point elements.

Fig. 4 The Veryst Proflex 30 compression material test specimen (left) and the FE mesh 

counterpart (right)
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The displacement time history for each compression test (all strain rates) was 

calculated from the known sample geometry and the true strain output from test, 

and served as the boundary condition for the FE simulation (while the opposite face 

of the specimen was fixed from displacing in the direction of the compression). The 

specimen is free to expand in the lateral x- and y-directions. The boundary 

conditions applied to the analyses were chosen to replicate the testing conditions as 

closely as possible. A simple schematic of the computational material compression 

test is shown in Fig. 5.

Fig. 5 Velodyne schematic for the Veryst compression testing

Based on the polymeric/rubber nature of these materials, the Corvid material fitting 

procedure employed an additive, nonlinear, hyper-viscoelastic constitutive model, 

where the stress is the sum of the hyperelastic stress model and the viscoelastic 

stress model:

σσ = σσhyyyy yy + σσvvvv . (1)

The additive split between hyperelastic and viscoelastic stress contributions 

provides the ability to solve for the deformation gradient, strain invariants, and 

strain rate tensor directly. Hyperelastic material models are typically described by 

strain energy density functions, ψψ, which is often a function of the principal 

stretches, λλ , or strain invariants, II . The strain energy density form, Eq. 2, for an 

Ogden rubber material is written in terms of the principal stretch components. The 

Ogden model16 is particularly useful for its relations to other existing models, as it 

reduces to the Mooney-Rivlin17 when mm = 2 and αα1,2 = 2, −2 and to the NeoHookean model18 when mm = 1 and αα1 = 2. This aspect gives it a broad range of 

applicability. 

ψψOOOO = ∑ �

μμmm

ααmm

�JJ

−ααmm 3� �λλ1

ααmm + λλ2ααmm + λλ3ααmm − 3��� mm=1 + KK

2 (JJ − 1)2. (2)
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In Eq. 2, μμmm and ααmm are the Ogden fitting parameters that can take on any real 

values, while the material parameter KK is a measure of the shear moduli, which 

must be a positive nonzero real value. 

The hyperelastic portion of the stress is calculated using the Ogden nonlinear elastic 

model as shown:

σσhyy = 1

JJ

FF �

∂∂ψψOOOOOOOOOO

∂∂EE �EE(ττ)��FFTT . (3)

The viscoelastic model by Li and Lau19 is as shown:

σσvvvv = 1

JJ

FF �∫ [AA1 + AA2(II2 − 3)]�∑ GG ee

−(tt−ττ)

TTii 6 �

=1 � EĖ(ττ) tt

0 � FFTT. (4)

The convolution integral was solved either through direct numerical integration or 

a state variables approach. Both methods were evaluated, but the state variable 

approach, which has better numerical efficiency with similar numerical error to that 

of the direct integration method, was used to produce all subsequent results. In 

Eq. 4, the viscoelastic model parameters GG and TT are the shear relaxation moduli 

and relaxation times, which make up the classical Prony series. A Prony-series 

expansion is a relaxation function approximation for modeling time-dependent 

damping. The scalar parameters AA1 and AA2 control the nonlinearity of the Prony 

series. Under the conditions AA1 = 1 and AA2 = 0, the model reduces to the standard 

Prony series viscoelastic model.

A 2-step (systematic calibration) material model parameter optimization procedure 

was employed for all materials. A systematic optimization was chosen given the 

quasistatic data and the additive nature of the material model in predicting stress 

(Eq. 1). The additive decomposition of the stress into hyperelastic and viscoelastic 

stresses allows for one to distinguish the viscoelastic effects from the hyperelastic 

effects by calibrating the material responses to the quasistatic data where strain 

rates become insensitive. For the hyperelastic parameters (Eq. 2), an optimization 

routine is performed for the material characterization test simulations at the lowest 

available compressive strain rate to establish the quasistatic behavior. These 

parameters were then locked for the rest of the process. Once the hyperelastic 

parameters are determined, a second optimization procedure is used to solve for the 

Prony series parameters (Eq. 4) that control the viscous dissipation. In this second 

step, all higher-rate tests are simulated to cover the full range of material rate effects 

over all available strain rates. These fits are then tested to verify the material 

parameter set, in addition to large deformation stability test simulations. If 

instabilities are indicated, then a lower order fit may be used as is the case with the 
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11

TC892 pelvic bone to preserve stability. This process was repeated for all the 

materials presented here, and the results are discussed in the following. 

Inverse analysis using nonlinear least-squares regression methods were applied to 

determine the material model parameters within Velodyne that best fit the 

experimental stress-strain data. To do so, the Design Analysis Kit for Optimization 

and Terascale Applications (DAKOTA),

20 a software package maintained by 

Sandia National Laboratories, was used to integrate Velodyne input and output with 

parallelization and optimization tools provided within DAKOTA and automate the 

linear regression process. Available worldwide under a GNU Lesser General Public 

License at no cost, DAKOTA offers several advantages over other optimization and 

integration software in that it provides parallel analysis and optimization tools that 

other facilities do not. Given the similar parallel capabilities of Velodyne, 

DAKOTA is a natural choice as an automated parallel iterator and decision maker 

when implemented on a high-performance cluster. 

The process flow for inverse analysis of parameter determination of a material 

model is shown in Fig. 6. After initialization, DAKOTA passes input to a Python 

script that updates material parameters for Velodyne. DAKOTA then spawns a 

number of Velodyne analyses on sets of separate processors, each of which can take 

advantage of parallel processing capabilities by using the individually allocated 

processors. Currently, these processors are allocated at the time an individual 

process is spawned, allowing reallocation of computational resource as needed. 

Upon completion, user-defined responses are calculated via a Python script. Then 

a stopping criterion (e.g., convergence value or maximum iteration number) is 

checked. If the check succeeds, output is written to files for postprocessing. If the 

check fails, a decision is made to update parameters via an optimization method 

through DAKOTA and the process iterates.
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Fig. 6 Process flow for inverse analysis using DAKOTA to iterate parallel runs of Velodyne

A standard response or objective function used for inverse analysis is the nonlinear 

least-squares response. For a data set containing stress versus strain data, the 

response ff is calculated as

ff = ∑ �σσAA(pp) − σσEE�

2

=1 , (5)

where σσAA(pp), a function of parameters pp, is the engineering stress at point i in strain 

found from the analysis and σσEE is the experimental value of the stress at strain i. 

An ideal response, representing a perfect fit of the experimental data with the 

material model, has a value ff = 0. For fitting multiple strain rates, the objective 

function becomes a sum of all the fitness values for each strain rate where the leastsquares response, R, was determined according to 

RR = ∑ ∑ �

�σσmm

AA (pp)−σσmmEE �

2

�

1/2

mm=1

NN

kk=1 , (6)

where N is the number of stress-strain histories used for calibration, n is the number 

of individual points a provided stress-strain history for curve k, σσmm

AA is the Cauchy 

stress at engineering strain EEmm

EE given by the model with parameters p, and σσmmEE is the 

experimental Cauchy stress at the same strain. 

The optimization problem is a nonlinear least-squares inverse analysis searching 

for a minimum to a multimodal objective function of Eq. 6 subject to various 

inequality constraints given by 

Initialization

Calculate 

Responses

Run Velodyne

Stopping 

Criterion Check

Post-Processing

Run Velodyne Run Velodyne

Update 

Velodyne 
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13

min RR(pp)

ssssssss ssss : GGllll ≤ GG ≤ GGuu

vvllll ≤ vv ≤ vvuu , (7)

where GG , is the initial tangent elastic shear moduli that should be bounded 

between a lower and upper bound based on material literature and the initial tangent 

modulus of the uniaxial stress-strain compression responses. Another nonlinear 

constraint to consider in the optimization of both rubbers and foams is that the 

Poisson ratio, vv should be bounded by lower and upper limits. For rubber materials, 

the Poisson ratio should be high enough for nearly incompressible behavior, which 

practical bounds were found to be between 0.450 ≤ vv ≤ 0.499. The Poisson ratio 

of a material can be calculated based on the bulk and shear modulus 

υυ = 3KK−2GG

6KK+2GG , (8)

such that for nearly incompressible material behavior, the bulk modulus should be 

significantly larger than the shear modulus, KK ≫ GG. Also, for rubber materials, 

incompressibility has been found to be essential in accurately predicting the 

viscoelastic behavior. In contrast, foam materials are much more compressible and 

the Poisson ratio has been found to be suitable between 0 ≤ vv ≤ 0.3. 

To update the parameters and control the process, an optimization algorithm was used 

as the decision maker. Each material model has a different level of complication in 

terms of number of parameters and sensitivity to change in parameters, making 

necessary the use of an algorithm that accounts for these issues while also considering 

computational and wall clock time costs. Historically, deterministic methods (e.g., 

methods that use derivatives to mathematically check for convergence) are largely 

computationally efficient, but they suffer from convergence issues, being easily 

trapped in local minima rather than finding a globally minimum response value. To 

alleviate some of these issues, heuristics methods are married with the deterministic 

algorithms, increasing the likelihood of obtaining a global minimum. On the other 

hand, nondeterministic methods (e.g., genetic and evolutionary algorithms) require 

large numbers of iterations, making them computationally much more expensive. 

However, they are often much more robust when combined with heuristics, often 

being able to find one or a number of global minima if they exist. 

In this study, the single objective genetic algorithm (SOGA) available in DAKOTA 

was used as the primary optimization algorithm for running the FE analysis of the 

actual samples in Velodyne. For the genetic algorithm, a population size of 100 points 

with 200 maximum number of generations specified giving a maximum of 20,000 

function evaluations. In addition, the deterministic quasi-Newton method available 

from the OPT++ package (optpp_q_newton) available in DAKOTA was explored in 
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14

conjunction with a multistart heuristic algorithm. The multistart algorithm chooses a 

specified number of starting points, 8 in this case, from the design space randomly, 

running separate optimizations from each point. For a single point, a maximum 

number of 100 iterations was specified. However, the deterministic algorithms in 

DAKOTA seem to be prone to premature convergence, thus the stochastic method 

of a genetic algorithm was leveraged more for optimization use in DAKOTA. 

3.2 Results for Velodyne Materials Models 

Using the approach outlined previously, the optimized material characterization 

parameters are presented for each material characterized by Veryst testing. The 

material parameters presented in this report have been validated well against 

subsystem and whole-body tests, and they were stable enough to run at durability 

and higher levels (Corvid validation document8

). A few iterations of material fits 

(not reported in the report) were required for some materials, for example, for the 

foot flesh, to overcome the instability issues in running durability and higher levels 

of loading simulations of the components or whole-body ATD tests. Additionally, 

a comparison of the model performance relative to experimental data is presented. 

Hyperelastic and viscoelastic Velodyne material model parameters and 

corresponding comparison of Ogden viscoelastic model response to experimental

data for 8 polymeric materials are shown in Tables 3‒18 and Figs. 7‒14, respectively. 

In general, the Ogden material model for the softer materials (pelvis flesh [Fig. 7], 

foot flesh [Fig. 8], and other flesh [Fig. 11]) fit well with experimental data for 

various strain rates. As for the harder plastics (foot plate [Fig. 9], butyl rubber [Fig.

12], tailbone [Fig. 13], and pelvis bone [Fig. 14]), the Ogden model did not predict 

responses at the higher strain rates as closely. It should be noted that for the harder 

plastic models, the higher-strain-rate predictions deviated from the respective 

experimental responses at larger strains due to complexity of the concurrent effects 

of viscoelastic and viscoplastic responses. A different material model, as is shown in 

the LS-DYNA case, could reduce the gaps between the simulation and experimental 

response at large strains, but at the cost of accounting for the viscoelastic effects at 

more WIAMan application relevant strains. Further refinement of the material model 

parameter estimation (for the Velodyne analyses) was not conducted to match the 

experimental response into the plastic strain regime of the test coupons mainly 

because the material models presented here produced excellent results within the 

elastic regime and acceptable results in the plastic regime. This assertion is supported 

by the successful validation of the WIAMan Velodyne model with in whole-body 

simulations6

, confirming that the ATD FEM model was capable of predictive models 

and ready to support the demanding nature of the applications need and meet the 

ATD design development milestone. 
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15

3.2.1 Proflex 30 Pelvis Flesh

Table 3 Hyperelastic fit parameters for the Proflex 30 pelvis flesh

ρ (kg/m3) μ1 

[MPa]

μ2

[MPa]

μ3

[MPa]

α1 α2 α3 K 

[MPa]

1040 –0.183 0.801 0.698 –1.425 –0.593 1.640 21.67

Table 4 Viscous fit parameters for the Proflex 30 pelvis flesh

G 1 (MPa) G 2 (MPa) G 3 (MPa) G 4 (MPa) G 5 (MPa) G 6 (MPa)

0.253 0.186 0.551 2.231 2.921 1.204

TT 11 (s) TT 22 (s) TT 33 (s) TT 44 (s) TT 55 (s) TT 66 (s)

95.687 7.576E-2 1.08E-4 5.40E-5 3.70E-5 5.82E-8

AA 11 AA 22

0.0713 0.0127

Fig. 7 Comparison of the Ogden viscoelastic model to experimental compression data for 

the Proflex 30 pelvis flesh
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3.2.2 XE1031 Foot Flesh

Table 5 Hyperelastic fit parameters for the XE1031 foot flesh

ρ 

(kg/m3)

μ1 

[MPa]

μ2

[MPa]

μ3

[MPa]

α1 α2 α3 K 

[MPa]

1060 0.414 –0.898 –0.974 0.295 –0.686 –0.964 20.0

Table 6 Viscous fit parameters for the XE1031 foot flesh

GG 11 (MPa) GG 22 (MPa) GG 33 (MPa) GG 44 (MPa) GG 55 (MPa) GG 66 (MPa)

0.459 0.011 0.310 2.76 4.04 4.13

TT 11 (s) TT 22 (s) TT 33 (s) TT 44 (s) TT 55 (s) TT 66 (s)

7.98 2.86E-2 9.11E-4 5.93E-4 9.10E-5 7.26E-7

AA 11 AA 22

0.011 0.000

Fig. 8 Comparison of the Ogden viscoelastic model to experimental compression data for 

the XE1031 foot flesh
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3.2.3 FD70 Foot Plate

Table 7 Hyperelastic fit parameters for the FD70 foot plate

ρ 

(kg/m3)

μ1 

[MPa]

μ2

[MPa]

μ3

[MPa]

μ4

[MPa]

μ5

[MPa]

α1 α2 α3 α4 α5 K 

[MPa]

1211 ‒14.595 37.595 ‒10.613 0.256 43.532 0.637 ‒5.883 1.632 ‒2.285 11.362 2500

Table 8 Viscous fit parameters for the FD70 foot plate

GG 11 (MPa) GG 22 (MPa) GG 33 (MPa) GG 44 (MPa) GG 55 (MPa) GG 66 (MPa)

42.45 66.66 98.72 95.89 30.096 99.96

TT 11 (s) TT 22 (s) TT 33 (s) TT 44 (s) TT 55 (s) TT 66 (s)

35.442 2.48E-2 1.747E-3 5.28E-4 9.64E-5 2.08E-7

AA 11 AA 22

1.000 0.192

Fig. 9 Comparison of the Ogden viscoelastic model to experimental compression data for 

the FD70 foot plate
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3.2.4 Delrin Calcaneus Cap

Table 9 Hyperelastic fit parameters for the Delrin calcaneus cap

ρ 

(kg/m3)

μ1 [MPa] μ2

[MPa]

μ3

[MPa]

α1 α2 α3 K 

[MPa]

GG00

[MPa]*

1410 363.0 762.0 121.0 8.72 –4.15 15.6 2310 942

Table 10 Viscous fit parameters for the Delrin calcaneus cap

G 1 (MPa) G 2 (MPa) G 3 (MPa) G 4 (MPa) G 5 (MPa) G 6 (MPa)

0.0719 80.3 18.4 83.9 3.29 93.4

TT 11 (s) TT 22 (s) TT 33 (s) TT 44 (s) TT 55 (s) TT 66 (s)

12.6 0.686 8.34E-03 7.97E-04 2.33E-05 5.10E-08

AA 11 AA 22

1 0.107

Fig. 10 Comparison of the Ogden viscoelastic model to experimental compression data for 

the Delrin calcaneus cap
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3.2.5 E1030AL Flesh (Other)

Table 11 Hyperelastic fit parameters for the E1030AL flesh

ρ (kg/m3) μ1 [MPa] μ2

[MPa]

μ3

[MPa]

α1 α2 α3 K 

[MPa]

1050 –0.227 –0.2478 0.6977 –1.426 –0.4571 0.271 22.07

Table 12 Viscous fit parameters for the E1030AL flesh

G 1 (MPa) G 2 (MPa) G 3 (MPa) G 4 (MPa) G 5 (MPa) G 6 (MPa)

0.4313 0.879 0.0341 4.625 2.327 1.070

TT 11 (s) TT 22 (s) TT 33 (s) TT 44 (s) TT 55 (s) TT 66 (s)

2.202 2.371E-3 2.215E-3 4.20E-4 8.28E-5 8.22E-7

AA 11 AA 22

0.220 0.000

Fig. 11 Comparison of the Ogden viscoelastic model to experimental compression data for 

the E1030AL flesh
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3.2.6 Butyl Rubber (75 Shore A) Compliant Elements

Table 13 Hyperelastic fit parameters for the butyl rubber 75A

ρ 

(kg/m3)

μ1 

[MPa]

μ2

[MPa]

μ3

[MPa]

α1 α2 α3 K 

[MPa]

1460 6.042 2.668 –3.854 5.845 –2.935 4.990 150

Table 14 Viscous fit parameters for the butyl rubber 75A

G 1 (MPa) G 2 (MPa) G 3 (MPa) G 4 (MPa) G 5 (MPa) G 6 (MPa)

1.952 11.238 41.270 47.886 24.999 49.863

TT 11 (s) TT 22 (s) TT 33 (s) TT 44 (s) TT 55 (s) TT 66 (s)

22.257 6.74E-2 5.314E-3 5.81E-4 8.70E-5 4.60E-7

AA 11 AA 22

1.000 0

Fig. 12 Comparison of the Ogden viscoelastic model to experimental compression data for 

the butyl rubber 75A
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3.2.7 Rencast 6425 Tailbone

Table 15 Hyperelastic fit parameters for the Rencast 6425 tailbone

ρ 

(kg/m3)

μ1 [MPa] μ2

[MPa]

μ3

[MPa]

α1 α2 α3 K 

[MPa]

1180 46.50 –25.76 52.20 16.98 –0.128 –7.864 1500

Table 16 Viscous fit parameters for the Rencast 6425 tailbone

G 1 (MPa) G 2 (MPa) G 3 (MPa) G 4 (MPa) G 5 (MPa) G 6 (MPa)

54.65 42.48 73.12 46.88 95.13 83.94

TT 11 (s) TT 22 (s) TT 33 (s) TT 44 (s) TT 55 (s) TT 66 (s)

5.577 0.6393 7.212E-2 3.955E-4 8.537E-5 1.699E-7

AA 11 AA 22

1 0.0636

Fig. 13 Comparison of the Ogden viscoelastic model to experimental compression data for 

the Rencast 6425 tailbone
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3.2.8 TC892 Pelvis Bone

Table 17 Hyperelastic fit parameters for the TC892 pelvis bone

ρ 

(kg/m3)

μ1 [MPa] μ2

[MPa]

μ3

[MPa]

α1 α2 α3 K 

[MPa]

1160 665 - - 2 - - 10000

Table 18 Viscous fit parameters for the TC892 pelvis bone

G 1 (MPa) G 2 (MPa) G 3 (MPa) G 4 (MPa) G 5 (MPa) G 6 (MPa)

1.819 0.843 1.485 26.4 36.893 47.234

TT 11 (s) TT 22 (s) TT 33 (s) TT 44 (s) TT 55 (s) TT 66 (s)

35.016 0.143 5.315E-2 3.33E-4 2.14E-5 6.61E-7

AA 11 AA 22

1.000 0.000

Fig. 14 Comparison of the Ogden viscoelastic model to experimental compression data for 

the TC892 pelvis bone
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4. LS-DYNA Material Models

The LS-DYNA material characterization was performed with multirate 

compression and tension testing on most of the plastic and rubber materials used in 

the dummy. Material models were created based on all of the available 

characterizations. Typically, an Ogden or Bergstrom-Boyce (BB) material model 

was used for soft materials such as the flesh. The material models were 

subsequently validated in the subassembly level validation. 

Table 19 features the polymer materials used in the LS-DYNA WIAMan model 

and lists where these materials are used; what material model is used to represent 

them; the strain rate range used to fit the material models; and the material library 

identification number.

Table 19 WIAMan LS-DYNA polymer materials

Material 

name

Anatomic 

location(s) LS-DYNA material model Strain rate range fitted

Material 

library ID

Butyl 

rubber 

75 Shore A

Compliant 

elements; 

spine rubber

*MAT_OGDEN_RUBBER T: -

C: 1-850 58

Proflex 30 Pelvis flesh *MAT_BERGSTROM_BOYCE_RUBBER T: 0.003-300

C: 0.01-950 59

E1030AL Flesh-other *MAT_BERGSTROM_BOYCE_RUBBER T: 1-90

C: 1-850 60

XE1031 Foot flesh *MAT_OGDEN_RUBBER T: -

C: 1-600 61

FD70 Foot plate *MAT_SIMPLIFIED_JOHNSON_COOK T: 1-75

C: 1-150 62

Delrin Calcaneus 

cap *MAT_SIMPLIFIED_JOHNSON_COOK T: 1-50C:40-600 63

TC892 Pelvic bone *MAT_SIMPLIFIED_JOHNSON_COOK T: 1-80

C: 1-550 64

Rencast 

6425 Tailbone *MAT_SIMPLIFIED_JOHNSON_COOK T: 1-300C: 1-160 65

ISODAMP Heel plug *MAT_OGDEN_RUBBER T: 1-300

C: 1-160 68

Note: T is tension and C is compression.

There are also several polymer materials used in the WIAMan that either require less 

fidelity than those listed previously or no test data were available for a material fit 

procedure to be performed. These materials were assigned Blatz-Ko Rubber material 

parameters based upon the durometer specified for the given materials. With the 

exception of the rubber representing the boot treads (inherited from the US Army 

Research Laboratory [ARL] in the boot model) and the molded neck rubber 

(optimized based upon experimental tests), the durometers were converted to elastic 

moduli (followed by a conversion to shear moduli) according to Qi et al.21 in Eq. 9):
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24

EE = 0.0235SS − 0.6403

SS = � SSh AA 20AA < SS < 80AA

SSh DD + 50 80AA < SS < 85DD

GG = EE

2(1+νν) . (9)

4.1 Polymer Material Models

Four different LS-DYNA polymeric material models (Bergstrom_Boyce, 

Ogden_Rubber, Simplified_Johnson_Cook, and Blatz_KO_Rubber) have been 

used in the LS-DYNA FE modeling of the WIAMan ATD. Final selection of the 

material models in the WIAMan FEM was based on the stability of the material 

model behavior over a variety of applied loading conditions. For example, 

BERGSTROM_BOYCE model showed poor correlation among the experimental 

and simulation results when compared in the cervical spine (compliant material) 

component model case. However, a change in the material model from 

BERGSTROM_BOYCE to the Ogden material model resulted in a much better 

correlation of simulation results as discussed in the polymer fitting procedure in 

Section 4.2. A brief outline of constitutive equations describing the fundamental 

behavior of the models are described next. 

4.1.1 *MAT_OGDEN_RUBBER

Hyperelastic materials are a class of elastic materials for which the stress-strain 

relationship is dependent upon a strain energy potential function; materials of this 

type can reach beyond standard linear elasticity in that the strain energy function 

provides for work-path independence and options for nonlinear elasticity and nearincompressibility. Rubber materials often exhibit hyperelastic qualities and 

therefore are often idealized as incompressible hyperelastic materials. The standard 

Ogden model is a well-known and commonly used hyperelastic constitutive model. 

Alone, the Ogden model cannot exhibit rate-dependent properties, but the addition 

of a viscoelastic material model superimposed upon the Ogden model allows for 

rate sensitivity. The LS-DYNA implementation22 has the option to add 

viscoelasticity to the Ogden model with a Prony series (a Maxwell fluid-type model 

consisting of springs and dampers in series) shown in the following equations.

HHHH HHHH OOOO MM : �

WW(λλ1, λλ2, λλ3) = ∑ μμpp

ααpp

�λλ1

ααpp + λλ2ααpp + λλ3ααpp − 3� NN

=1

σσjj = pp + λλjj

∂∂∂∂

∂∂λλjj

,

(10)
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25

with WWas the strain energy potential as a function of the principal stretches λλ ; pp as 

the pressure; μμ , αα , and NN as material constants; and σσjj as the principal Cauchy 

stresses.

VV PP SS :�

σσ = ∫ ( − ττ)

∂∂εεkkkk

∂∂ ∂∂ tt

0

( ) = ∑ GG ee−ββiitt =1

, (11)

with σσ as the Cauchy stresses, as time, GG as shear moduli, and ββ as decay 

constants.

4.1.2 *MAT_BERGSTROM_BOYCE_RUBBER

The BB material model is a viscoplastic model, consisting of Arruda-Boyce 8-chain 

hyperelastic models and a viscous flow model. The Arruda-Boyce model is a 

hyperelastic polymer model based upon statistical mechanics and the finite 

extensibility of a polymer chain.

23 Its rheological representation is that of parallel 

paths A and B, each containing an Arruda-Boyce hyperelastic “spring”, but with a 

viscous damper placed in series with the spring in Path B. The deviatoric Kirchhoff 

stress is computed as shown in the following equations:

ττ� = ττAA + ττBB

EE PP h AA

⎩

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎧ ττAA = GG

3

3−λλrr

2

1−λλrr

2 �bb� − TT �bb��

3

II�

G is the elastic shear modulus,

bb� = JJ−2⁄3FFFFTT

JJ = det(FF)

is the unimodular left Cauchy Green tensor, and

λλ2 = TT �bb��

3NN

is the relative network stretch

(12)
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26

VV PP h BB

⎩

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎧

Perform a multiplicative split of the deformation gradient into

elastic and inelastic parts

JJ1⁄3FF = FFeeFFii

bbee = FFeeFFee

TT

ττBB = GGvv

3

3−λλvv

2

1−λλvv

2 �bbee − TT (bbee)

3

II�

This time Gv is the shear modulus for Path B,the relative

network stretch is

λλvv

2 = TT (bbee)

3NNvv

the left Cauchy Green Tensor is evolved via

bḃ

ee = LL�bbee + bbeeLL�TT − 2DDiibbee

the inelastic rate of deformation tensor is

DDii = γγ̇

0(λλ − 0.999) �

‖ττBB‖

ττ�√2 �

mm ττBB

‖ττBB‖

λλ2 = TT �FFii

TTFFii�

3 ≥ 1

and the deviatoric velocity gradient is

LL� = LL − TT (LL)

3

II

(13)

4.1.3 *MAT_SIMPLIFIED_JOHNSON_COOK

The Johnson-Cook material model is an elastic-plastic constitutive equation. Its 

advantage is a simple empirical implementation of strain, strain rate, and heatdependent plasticity. There are several polymers in the WIAMan that behave as 

hard plastics, showing a linear, rate-independent stress-strain relationship in the 

small-strain elastic range followed by rate-dependent yielding behavior in the larger 

strain ranges. The LS-DYNA simplified Johnson-Cook model22 saves 

computational time by stripping the thermal effects away from the original 

Johnson-Cook equation, leaving only the strain hardening and strain-rate scaling 

components for calculation of flow stress shown in the following equations:

σσff = (AA + BBεε̅ )(1 + ln εε̇

∗), (14)

nn ee ee ee ssss ss : εε̇

∗ = εε�̇

εε̇

0

, (15)

where A is the initial yield stress of the material; B and n are material constants that 

account for strain hardening; and c is a material constant for strain-rate scaling. The 

strain rate used in the scaling is normalized by the quasistatic threshold strain rate, 

εε0̇ , commonly the lowest strain rate for which material data were provided, but 

sometimes tuned to provide for the best match to material data.
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27

4.1.4 *MAT_BLATZ-KO_RUBBER

The Blatz-Ko model is a simple hyperelastic constitutive equation commonly used 

to represent rubber materials. The LS-DYNA implementation fixes the Poisson’s 

Ratio, νν, at 0.463 to represent a nearly incompressible rubber,

22 leaving the user 

only the shear modulus, G, as a necessary input to the model. Cauchy stress is 

computed using the left Cauchy-Green strain tensor, B, and the determinant of the 

deformation gradient, J:

σσ = GG �

1

JJ

BB − JJ

− 1

1−2υυII�. (16)

4.2 Polymer Fitting Procedure

Generally, the first attempt at material fitting of the soft polymers was the BB 

model. The BB formulation has the advantage of being truly viscoplastic, 

accounting for rate dependence beyond the elastic realm.

23 Its accuracy has also 

been demonstrated for a number of engineering rubbers and softer biomaterials.

23

The material model is based upon a micromechanics approach to polymer systems, 

so soft polyurethane materials such as the various flesh models in WIAMan fit 

readily into the BB material template. However, as in the case of the 75 Shore A 

butyl rubber, the BB model had a difficult time conforming to the experimental data 

provided. For this situation, we turned to the Ogden + Prony Series model. This 

viscoelastic model bases itself upon empirical high-order polynomial fits and is 

thus readily adaptable to many curve shapes. As shown in Fig. 15, the Ogden + 

Prony Series model is able to accurately capture the rate-dependent behavior of the 

butyl rubber, while BB falls short.
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Fig. 15 BB fit for butyl rubber (top) vs. Ogden+Prony fit (bottom) at strain rates of 1 s–1

(red) and 50 s–1 (green)

There were also situations during the development of this model where LS-DYNA 

seemed to be less stable while using the BB model in confined areas during higher 

loading conditions, such as the strength-of-design (SoD) load case. This may be 

attributed to the contact algorithms exciting the material into a frenzied state. In 

some situations, such as in the foot flesh, switching the material formulation from 

BB to Ogden + Prony can help to stabilize the solution. While the Ogden + Prony 

model may provide a more stable solution, it is decidedly less accurate than the BB 

model, as shown in Fig. 16. In this figure, the simulated right tibia and calcaneus 

forces are compared to experimental data for 2 loading conditions, a severe SoD 

loading case and a low intensity target input (WH1a) for subinjurious UBB 

loading.

24 For the SoD case, the ATD was subjected to 18-m/s impact velocity and 

for the WH1a case, the ATD was subjected to 4-m/s impact velocity. 
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SoD Bergstrom-Boyce

SoD Ogden+Prony

WH1a Bergstrom-Boyce

WH1a Ogden+Prony

Fig. 16 Performance results of the tibia and calcaneus load cells during SoD and WH1a load 

cases using different foot flesh material models
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4.2.1 MCalibration Software

For most of the polymer materials, Veryst’s MCalibration material fitting 

software25 was used to fit the material model variables to experimental data.

23 By 

default, the software uses an internal FEM solver to apply experimental strain-time 

history to a single FE, comparing the computed element stress response to the 

experimental stress response while iterating upon the material variables. Since the 

BB and Johnson-Cook models come preloaded into MCalibration, this is the 

method used to compute them. 

For material models that are not preloaded into MCalibration (e.g., Ogden with an 

added Prony Series, the software has the option for users to add other LS-DYNA 

material models and solve them with the LS-DYNA solver). For this process, 

MCalibration inserts the strain-time history of the loaded experimental results into 

a LS-DYNA input file that includes commands to run a single-element test, similar 

to the way its own default solver operates. MCalibration inserts new material 

information for each optimization iteration into the LS-DYNA input deck and 

submits it to the LS-DYNA solver, retrieving the results and comparing them to the 

experimental stress history.

The default optimization process for MCalibration uses several different 

optimization schemes including an initial random search followed by LevenbergMarquardt, NEWUOA, Nelder-Mead Simplex, genetic algorithm, and others.

25 The 

optimization schemes are cycled until a converged solution is found, a maximum 

run time is reached, or the user manually ends the run. The default fitness score 

used to determine quality and convergence is the normalized mean absolute 

difference (NMAD):

NN = 〈�σσ − σσ ee �〉

〈�σσ ee �〉 � . (17)

While NMAD is used by the program as a means to evaluate the fit during the 

optimization process, a more recognizable curve fitness value is shown on the 

plotted results, the coefficient of determination or R2 value, for which a value of 

1.0 would represent an exact match to experimental data: 

RR2 = 1 − ∑ �σσ − σσ ee �

2

=1

∑ �σσ ee − 〈σσ ee 〉� =1

� . (18)

Note that 〈σσ〉 indicates the arithmetic mean of the values contained in vector σσ and 

|σσ| indicates the magnitude of each value contained in vector σσ.
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4.2.2 LS-OPT Software

Another program available for material fitting operations is LSTC’s LS-OPT 

program. LS-OPT was created as a general-purpose optimization program for LSDYNA. Among LS-OPT’s features is a curve mapping algorithm designed with 

material fitting in mind. For models that have difficulty fitting in MCalibrate (e.g., 

Delrin in the WIAMan material library), LS-OPT provides another robust option 

that uses LS-DYNA as its base FEM solver. A modeler builds and submits a fully 

functional LS-DYNA model and tags features of the model for LS-OPT to set as 

variables in its optimization. Material variables are marked in the LS-DYNA input 

deck and LS-OPT approaches the problem by either direct simulation via a genetic 

algorithm (GA) or building a metamodel from strategically chosen points in the 

variable design space. The GA approach was selected for finding the properties of 

the Delrin material model, since it proved very robust when certain combinations 

of variables in the design space caused simulations to fail before completion. 

GAs approach the problem in much the same way as biological genetic evolution, 

optimally sampling the design space to create a starting set, and then selecting the 

fittest of the group to combine attributes and act as parents of a new generation of 

samples. A probability of mutation creates the ability for random variation to occur 

within the generations without influence from the fittest samples of the previous 

generation. The method is robust, but can be time consuming with large or longrunning models since many individual simulations must be run to converge upon a 

solution. Since the simulations for material fitting only included 8-element models, 

running many simulations was not a barrier to the solution.

The Delrin fitting solution was approached with an 8-element block instead of the 

usual single-element simulation. The fit solution was unstable for this particular 

material when only one element was used in the optimization process; switching to 

LS-OPT using multiple elements solved this problem.

4.2.3 Molded Neck Rubber Fit Procedure

The molded neck rubber received its own fit procedure. Material characterization 

data were not available; however, isolated WIAMan neck experiments had been 

performed at Duke University. Replicating the Duke experimental setup in a LSDYNA FEM, a team at the Wake Forrest Center for Injury Biomechanics optimized 

the shear modulus of a Blatz-Ko model (Table 20) to fit the force-time histories 

between the model and the experiment.
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Table 20 Blatz-Ko fit parameters for select WIAMan polymers

Material 

Library 

ID

Name Use ρ

(kg/m3)

G 

(MPa)

23 Black Natural Rubber 70 Shore A shoulder stops 930 3.45

25 Black Neoprene Rubber 65 Shore A arm stops 1,230 2.64

26 Black Neoprene Rubber 80 Shore A elbow compression 

washers 1,230 5.94

27 Black Neoprene Rubber 40 Shore A elbow and knee stops 1,230 0.68

32 Tan Polyurethane 70 Shore D leg DAS covers 1,140 51.69

36 Black SBR Rubber 75 Shore A upper leg absorber 

washer 940 4.53

48 Euro Brown Urethane 80 Shore A upper arm “Z” stop 1,070 5.94

49 Euro Brown Urethane 95 Shore A lower leg stops; elbow 

pin washers 1,130 10.20

51 Polyurethane Skull 75 Shore D skull 1,140 67.75

67 Optimized Molded Neck Rubber 45 

Shore A molded neck 1,180 1.96

975 Left Boot Tread Rubber boot tread 1000 15

983 Right Boot Tread Rubber boot tread 1000 15

4.3 Polymer Fitting Results

4.3.1 Butyl Rubber 75 Shore A Compliant Elements and Spine Rubber

This material was fit to the native LS-DYNA Ogden rubber model with viscoelastic 

Prony Series (Table 21 and Fig. 17). The characterization data were obtained from 

Veryst and the software MCalibrate was used to fit the characterization data to the 

material model. A material model provided by Corvid was used as a basis for 

MCalibrate to further tune the constitutive properties to LS-DYNA’s Ogden model.

Table 21 Butyl rubber 75 Shore A material parameters

ρ

(kg/m3) ν μ1 (MPa) μ2 (MPa) μ3 (MPa) α1 α2 α3

1460 0.486 6.042 2.668 –3.854 5.846 –2.935 4.99

G1

(MPa) G2 (MPa) G3 (MPa) G4 (MPa) G5 (MPa) G6 (MPa)

1.3592 2.3781 8.8524 11.0872 61.6273 640.2614

β1 (1/s) β2 (1/s) β3 (1/s) β4 (1/s) β5 (1/s) β6 (1/s)

1.9735 1025.2649 386.2772 1099.9231 9103.8316 5203539
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Fig. 17 Butyl rubber 75 Shore A material fit

4.3.2 Proflex 30 Polyurethane Pelvis Flesh

This material was fit to the native LS-DYNA BB model (Table 22 and Fig. 18). 

The material characterization and fitting were performed by Veryst.

Table 22 Pelvis flesh material parameters

ρ (kg/m3) K (MPa) G (MPa) Gv (MPa) n nv

1035 10 0.3298 0.03944 17.6804 2.7016

C m γ0 (s) τh (s)

–0.37317 2.37689 1 0.1367
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Fig. 18 Pelvis flesh material fit

4.3.3 E1030AL Polyurethane Arm, Leg, and Abdomen Flesh

This material was fit to the native LS-DYNA BB model (Table 23 and Fig. 19). 

The characterization data were obtained from Veryst and the software MCalibrate 

was used to fit the characterization data to the material model.

Table 23 Arm, leg, and abdomen flesh material parameters

ρ (kg/m3) K (MPa) G (MPa) Gv (MPa) n nv

1050 10 0.40045 0.79822 39.407626 49.731324

C m γ0 (s) τh (s)

–1.1395535 1.3164482 1 0.091117
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Fig. 19 Arm, leg, and abdomen flesh material fit

4.3.4 XE1031 Polyurethane Foot Flesh

This material was fit to the native LS-DYNA Ogden rubber model with viscoelastic 

Prony series (Table 24 and Fig. 20). The characterization data were obtained from 

Veryst and the software MCalibrate was used to fit the characterization data to the 

material model.

Table 24 Foot flesh material parameters

ρ 

(kg/m3) ν μ1 (MPa) μ2 (MPa) μ3 (MPa) α1 α2 α3

1063 0.4 1.0652 0.0013381 0.22052 1.4941506 11.399695 –1.224465

G1

(MPa) G2 (MPa) G3 (MPa) G4 (MPa) G5 (MPa)

0.016304 0.11873 0.20649 0.72263 0.035175

β1 (1/s) β2 (1/s) β3 (1/s) β4 (1/s) β5 (1/s)

101.7071 1044.1123 1045.9716 1211.4211 11002.213
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Fig. 20 Foot flesh material fit

4.3.5 FD70 Polyurethane Foot Plate

This material was fit to a Johnson-Cook model (Table 25 and Fig. 21). The 

characterization data were obtained from Veryst and the software MCalibrate was 

used to fit the characterization data to the material model.

Table 25 Foot plate material parameters

ρ (kg/m3) E (MPa) ν vp ε0 (s)

1210 600.2922 0.35 1.0 1.9352

A (MPa) B (MPa) n C

20.9541 96.1332 0.791049 0.18333
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Fig. 21 Foot plate material fit

4.3.6 Delrin Calcaneus Cap

This material was fit to the native LS-DYNA Simplified Johnson-Cook model 

(Fig. 22 and Table 26). The characterization data were obtained from Veryst and 

the software LS-OPT was used to fit the characterization data to the material model.

Table 26 Calcaneus cap material parameters

ρ (kg/m3) E (MPa) ν vp ε0 (s)

1410 2543.45 0.35 1.0 1.4229

A (MPa) B (MPa) n C

39.5381 85.0114 1.53765 0.189606
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Fig. 22 Calcaneus cap material fit

4.3.7 TC892 Polyurethane Pelvic Bone

This material was fit to a Johnson-Cook model (Fig. 23 and Table 27). The 

characterization data were obtained from Veryst and the software MCalibrate was 

used to fit the characterization data to the material model.

Table 27 Pelvis bone material parameters

ρ (kg/m3) E (MPa) ν vp ε0 (s)

1160 1924.4343 0.4 0.0 1.0655

A (MPa) B (MPa) n C

53.8458 98.7793 0.3581026 0.0688742

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 Engineering Stress (MPa)

Engineering Strain

Model Rate 1

Model Rate 50

Model Rate 40

Exp Rate 1

Exp Rate 50

Exp Rate 40
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Fig. 23 Pelvis bone material fit

4.3.8 Rencast 6425 Polyurethane Tailbone

This material was fit to a Johnson-Cook model (Fig. 24 and Table 28). The 

characterization data were obtained from Veryst and the software MCalibrate was 

used to fit the characterization data to the material model.

Table 28 Tailbone material parameters

ρ (kg/m3) E (MPa) ν vp ε0 (s)

1180 716.8913 0.46 1.0 1.2861

A (MPa) B (MPa) n C

21.5051 22.4628 0.3478949 0.136802
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Fig. 24 Tailbone material fit

4.3.9 ISODAMP Heel Plug

This material was fit to the native LS-DYNA Ogden rubber model with viscoelastic 

Prony series (Fig. 25 and Table 29). The characterization data were obtained from 

ARL and the software MCalibrate was used to fit the characterization data to the 

material model.

Table 29 Heel plug material parameters

ρ 

(kg/m3) ν μ1 (MPa) μ2(MPa) μ3 (MPa) α1 α2 α3

1290 0.49 0.4327 0.55538 –0.5700 –1.183380 –0.689722 –4.974810

G1

(MPa)

G2

(MPa) G3 (MPa) G4(MPa) G5 (MPa)

0.46338 0.093381 0.0060828 1.6867 123.874

β1 (1/s) β2 (1/s) β3 (1/s) β4 (1/s) β5 (1/s)

0.57718 777.275 435.748 1248.84 23248.699
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Fig. 25 Heel plug material fit

5. Typical WIAMan Strain Rate Environment

As mentioned previously, material models developed by both teams used available 

strain-rate test data ranging from quasistatic to 1,000 strain/s (where s is second), 

when applicable, in their material model parameters extraction algorithms. 

Simulation results indicated that the inclusion of very high-strain-rate effects 

(above 150 strain/s) was more than adequate for the WIAMan ATD modeling since 

typical strain rates in WIAMan model simulations did not exceed 150 strain/s. 

Materials for the TD were tested at higher rates based on estimated strain rates 

reported for Hybrid 3 simulations by Malone.

26 Future testing of new polymeric 

materials for the next-generation ATD could be tested at a much lower strain rates 

than 1,000 strain/s given no changes in the WIAMan loading environment. 

Figures 26–28 show the strain-rate data from 2 whole-body simulations of the ATD 

tests due to vertical accelerative loading. Details of the test configurations for the 

whole-body tests and simulation results are available in the literatures.

6,7 The 

whole-body test results came from the APL VALTS tests that impacted the seat and 

the floor at prescribed velocity profiles associated with a peak velocity and a time 

to peak (TTP) based on the target input conditions for subinjurious UBB loadings 

used for the WIAMan biomechanical research investigations. The first simulation 
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(Fig. 26) was from WH1a level tests in which the ATD with no personal protective 

equipment [PPE]) was tested at the APL VALTS for a loading profile having an 

amplitude of 4 m/s at a 5-ms TTP. Both floor, and seat were subjected to the 

amplitude and the TTP with different loading profiles discussed in the simulation 

results section. Figures 27 and 28 show the strain-rate data extracted from WH2a 

(without PPE) and WH2b (with PPE) level tests, for a peak velocity of 6 m/s at a 

5-ms TTP floor, and 4 m/s at a 10-ms TTP seat. PPE included helmet, body armor 

vest, and boot. Further details of the whole-body test conditions and the associated 

results are available in literature by Pietsch et al.24 All materials were fit to their 

models within this range, many including data well beyond 150 strain/s, and are 

thus relevant for both typical and extreme load cases. As indicated in 

Figs. 27 and 28, a maximum strain rate of 150 strain/s was observed in the heel 

flesh for both test conditions. 

Fig. 26 Strain rates experienced by soft polymers during the VALTS test at WH1a levels 

(4 m/s at a 5-ms TTP floor, and seat, no PPE)
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Fig. 27 Strain rates experienced by soft polymers during the VALTS test at WH2a levels 

(6 m/s at a 5-ms TTP floor, 4 m/s at a 10-ms TTP seat, no PPE)

Fig. 28 Strain rates experienced by soft polymers during the VALTS test at WH2b levels 

(6 m/s at a 5-ms TTP floor, 4 m/s at a 10-ms TTP seat, with PPE)
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6. Whole-Body ATD Model Simulation Results

Illustrative examples of the system-level, whole-body model performance of the 

material models described previously—by both modeling teams—are presented. 

The whole-body ATD experimental tests data came from the APL VALTS. The 

VALTS is a vertical impact allowing laboratory testing of various UBB loading 

profiles and scenarios. The system is capable of independent loading of the legs 

and pelvis of a seated ATD. Input loads were characterized by the peak velocity 

and TTP of the floor and seat independently. Total mass of the WIAMan TD FE 

model was 79.8 kg for the LS-Dyna case and 83.88 kg for the Velodyne model

compared to the mass of the physical prototype of 82.7 kg, which included external 

sensor wiring not present in the model.

The physical WIAMan TD with boots was tested experimentally at different impact 

velocities on the uncushioned VALTS rig. System validation was based on 

experimental testing and paired simulations of the WIAMan for the following 

conditions: 

• WH1a = 4 m/s at 5 ms TTP floor, 4 m/s at 5 ms TTP seat, no PPE

Several repeat tests at each velocity were run to investigate repeatability, but only 

a single case from each test series was used for validation. The WH1A condition is 

the lower velocity of the 2 cases yet with shorter TTP velocities, where the table 

(to which the throne is mounted) is driven to 4.5 m/s at 5 ms TTP and the floor 

reached 4.1 m/s at 4 ms TTP. The velocity histories were captured in test via a hard 

mount accelerometer on the table and floor plates, respectively, and subsequently 

integrated into velocity histories. The velocity boundary conditions employed for 

each simulation are shown in Fig. 29.
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Fig. 29 Velocity history from the WH1A and WH2A VALTS tests that are employed as the 

simulation boundary conditions

Both simulations (LS-DYNA and Velodyne) of the WH1A case were carried out 

and the computational sensors histories were captured for validation (Figs. 30–34

and Table 30). Response metrics for the over 30 sensors were aggregated using 

Correlation and Analysis (CORA; version 3.6) to compute a composite score.

CORA measures the correlation of simulation versus test responses on a scale of 0 

to 1, where 0 represents no correlation and 1 represents perfect correlation of 

response signals. A CFC 600 filter is applied to all force and moment signals and a 

CFC 1000 filter is applied to all accelerometer signals. Model validation results 

from the paired tests were compared using CORA, which numerically assesses the 

magnitude, shape, and phase of similar response signals to obtain objective 

metrics.

27 Each entry in Table 30 is color coded on a scale from red (a score of 0.0) 

to green (a score of 1.0). In general, based on average CORA scores of greater than 

0.65 in conjunction with the engineering judgement of the WIAMan M&S team, 

the WIAMan model is considered to be validated for these nominal impact cases.

24
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Fig. 30 Match pair validation results for the lower extremity at the heel and mid-tibia sensor 

regions for the simulation and the experiment under the WH1a test condition

Fig. 31 Match pair validation results for the lower and upper neck sensor regions for the 

simulation and the experiment under the WH1a test condition
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Fig. 32 Match pair validation results for the lower extremity at the femur and tailbone 

sensor regions for the simulation and the experiment under the WH1a test condition
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Fig. 33 Example cross-plots of the Velodyne simulation and test for WH1A (neck calcaneus 

and tibia)
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Fig. 34 Example cross-plots of the Velodyne simulation and test for WH1A (femur and 

tailbone)
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Table 30 CORA summary table for the WIAMan TD WH1A Velodyne simulations 

7. Conclusions

The material characteristics parameters specific to the 2 FEM codes (LS-DYNA 

and Velodyne) for 8 polymeric materials used in key components in the WIAMan 

ATD TD were presented in this report. Both material characterization schemes used 

the experimentally derived multirate compression and tension material test data 

from the same source to extract material model parameters for their respective 

analytical ATD models. Material models were created based on a number of 

available characteristics models. Typically, an Ogden or BB material model was 

used for the soft materials. Simulation results indicated that typical strain rates in 

the WIAMan ATD do not exceed 150 strain/s for typical severe and subinjurious 
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UBB loadings environment for which the WIAMan ATD has been designed. Future 

testing of new polymeric materials for the next-generation ATD could be tested at 

a much lower strain rates than 1,000 strain/s given no changes in the WIAMan 

loading environment. 

The material models were subsequently validated in the subassembly level 

validation. There is room for improvement in the material model fitting process; 

however, because of the good comparison (acceptable to a degree that serves the 

purpose of evaluating the evolving ATD design iterations) of experimental and 

simulation results for whole-body test cases, the model parameters extracted in the 

report were deemed appropriate. Intra- and intercomparisons of model simulation 

results for both FE codes with the identical experimental test cases indicated good 

correlations. The use of 2 FE codes in solving an identical simulation environment 

also provided an opportunity to extract two data points for the same simulation 

environment thus providing an increased degree of confidence in the model 

predictability. Finally, a brief summary of the whole-body simulation results (both 

models) of an ATD response due to vertical accelerative loading were compared 

for the same experimental data to document the predictive capability of material 

models. 
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8. References

1. Warrior Injury Assessment Manikin (WIAMan). Washington (DC): dgMarket; 

2016 May 9 [accessed 2016]. http://www.dgmarket.com/tenders/npnotice.do?noticeId=13763702.

2. Hoppel C. et al. Workshop on numerical analysis of human and surrogate 

response to accelerative loading. Aberdeen Proving Ground (MD): Army 

Research Laboratory (US); 2014 May. Report No.: ARL-SR-287.

3. Prevention, mitigation, and treatment of blast injuries. Ft Detrick (MD): DOD 

Blast Injury Research Program Coordinating Office. Science & technology 

Efforts & Programs, Army Medical Research & Material Command (US); 

2014. FY14 Report to the Executive Agent.

4. Kleinberger M. et al. Second workshop on numerical analysis of human and 

surrogate response to accelerative loading. Aberdeen Proving Ground (MD): 

Army Research Laboratory (US); 2016.

5. Chancey C, McEntire J, Scherer R, Frounfelker P, Tegtmeyer M. Program for 

Warrior Injury Assessment Manikin (WIAMan). Aberdeen Proving Ground 

(MD): Army Research Laboratory (US); 2011.

https://blastinjuryresearch.amedd.army.mil/docs/WIAMan_Project_Plan_Ind

ustry_Day_V3.pdf .

6. Bell C, Lister K, Shirley A, Chowdhury M. Validation of a whole body 

WIAMan model for vehicle survivability, Ground Vehicle Survivability 

Training Symposium (GVSTS); 2016 Nov 5–17; Ft Benning, GA.

7. Armiger R, Boyle M, Gayzik S, Merkle M, Chowdhury M. The development 

of a virtual WIAMan for predicting occupant injury and vehicle performance, 

ground vehicle survivability training symposium (GVSTS); 2016 Nov 15–17; 

Ft Benning, GA. 

8. Bell C, Lister K, Nochetto H, Robeck C, Yow C. User’s manual and validation, 

WIAMan Velodyne Model ‒ TDv1.2. Mooresville (NC): Corvid Technologies;

2016 Jun 30.

9. Vavalle N, Shanaman M, Lomicka C, Boyle M, Armiger R. User’s manual and 

validation summary; WIAMan ATD Tech Demonstrator LS-Dyna FEM 

v1.0.0. Laurel (MD): Johns Hopkins Applied Physics Lab; 2016.

10. Ott K, Dooley C, Wickwire A, Iwaskiw A, Armiger R, Merkle A. Initial 

characterization of the human response to vertical accelerative loading.

Seventh World Congress of Biomechanics; 2014 Jan 15; Boston, MA.
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11. Sanborn B, Moy P, Mrozek R, Weerasooriya T. Effect of strain rates on the 

compressive response of neck rubber from humanetics HIII 50th percentile,

male dummy under different loading sequences. Aberdeen Proving Ground 

(MD): Army Research Laboratory (US); 2013 Feb. Report No.: ARL-TR6336.

12. LS-DYNA Support, Material models for polymers. Livermore (CA):

Livermore Software Technology Corporation; 2016 [accessed 2016].

http://www.dynasupport.com/howtos/material/material-models-for-polymers.

13. LS-DYNA keyword user’s manual volume II, material models (revision: 

1275). Livermore (CA): Livermore Software Technology Corporation; 2012 

Mar 26. 

14. Jeong D, Kwok P, Canha J. Characterization of deformable materials in the 

THOR dummy, injury Science Research Proceeding of the 28th International 

Workshop; 2000 Nov; Atlanta, GA. 

15. Crawford DM, Chowdhury MR, Pietsch HA. Mechanical properties of 

polymers used for anatomical components in the Warrior Injury Assessment 

Manikin (WIAMan) Technology Demonstrator. White Sands Missile Range 

(NM): Army Research Laboratory (US); 2016 July. Report No.: ARL-TR7728. 

16. Ogden RW. Large deformation isotropic elasticity-on the correlation of theory 

and experiment for incompressible rubberlike solids. Proc Royal Society of 

London A: Mathematical, Physical and Engineering Sciences

1972;326(1567):565–584. The Royal Society.

17. Mooney M. A theory of large elastic deformation. J Applied Physics.

1940;11(9):582–592.

18. Bower AF. Applied mechanics of solids. Boca Raton (FL): CRC press; 2009.

19. Li C, Lua J. A hyper-viscoelastic constitutive model for polyurea. Materials 

Lett. 2009;63(11):877–880.

20. Dakota Version 5.4 user’s manual. Albuquerque (NM): Sandia National 

Laboratories; 2014.

21. Qi HJ, Joyce K, Boyce MC. Durometer hardness and the stress-strain behavior 

of elastomeric materials. Rubber Chem and Tech. 2003;76.

22. LS-DYNA keyword user’s manual. Vol. II. Livermore (CA): Livermore 

Software Technology Corporation; 2015. 
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23. Bergstrom J. Mechanics of solid polymers theory and computational modeling. 

San Diego (CA): William Andrew; 2015.

24. Pietsch HA. et al. Evaluation of WIAMan technology demonstrator biofidelity 

relative to sub-injurious PMHS response in simulated under-body blast events.

Stapp Car Crash J. 2016;60. Submission 16S-27,

25. PolyUMod and MCalibration software. Needham Heights (MA):Veryst 

Engineering; 2015.

26. Malone D. Validation and updating of the gen2 LS-DYNA model of the H-III 

ATD (50th percentile). UBM FY14 Task 6.1. Aberdeen Proving Ground 

(MD): Army Research Laboratory (US); 2014 Apr. 

27. Ghere C, Gades H. Objective rating of signals using test and simulation 

responses. 21st Enhanced Safety of Vehicles; 2009; Stuttgart, Germany.
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List of Symbols, Abbreviations, and Acronyms

ARL US Army Research Laboratory

ATD anthropomorphic test device

BB Bergstrom-Boyce

DAKOTA Design Analysis Kit for Optimization and Terascale Applications

DOT&E Director, Operational Test and Evaluation

EO Engineering Office

FEM finite-element model

GA genetic algorithm

Gen generation

JHU-APL Johns Hopkins University Applied Physics Laboratory

LFT&E live-fire test and evaluation

M&S modeling and simulation

N-T UBB Near-Term Under-body Blast

PPE personal protective equipment

SOGA single objective genetic algorithm

SoD strength of design

TD Tech Demonstrator

TTP time to peak

UBB under-body blast

V&V validation and verification

VALTS Vertically Accelerated Load Transfer System

WIAMan Warrior Injury Assessment Manikin
Approved for public release; distribution unlimited.

56

1 DEFENSE TECHNICAL

(PDF) INFORMATION CTR

DTIC OCA

2 DIRECTOR

(PDF) US ARMY RESEARCH LAB

RDRL CIO L

IMAL HRA MAIL & RECORDS

MGMT

1 GOVT PRINTG OFC

(PDF) A MALHOTRA

2 TARDEC

(PDF) RDTA RS

R SCHERER

H PIETSCH

14 DIR USARL

(PDF) RDRL DPW

M CHOWDHURY

D CRAWFORD

F HUGHES

J TICE

RDRL WMM G

J LENHART

RDRL WMP F

N GNIAZDOWSKI

E FIORAVANTE

D KRAYTERMAN 

RDRL SLB E

C BARKER

M MAHAFFEY

D HOWLE

RDRL WMP G

S KUKUCK

RDRL WMP B

C HOPPEL

T WEERASOORIYA