Experimental Validation of the Butyl-Rubber Finite Element 

(FE) Material Model for the Blast-Mitigating Floor Mat

by Masayuki Sakamoto

ARL-SR-0329 August 2015 

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Army Research Laboratory

Adelphi, MD 20783-1138

ARL-SR-0329 August 2015 

Experimental Validation of the Butyl-Rubber Finite Element 

(FE) Material Model for the Blast-Mitigating Floor Mat

Masayuki Sakamoto

Japanese ESEP Research Engineer 

at Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution unlimited. 
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4. TITLE AND SUBTITLE

Experimental Validation of the Butyl-Rubber Finite Element (FE) Material 

Model for the Blast-Mitigating Floor Mat

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6. AUTHOR(S)

Masayuki Sakamoto 

(Japanese Engineer Scientist Exchange Program Research Engineer)

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ESEP

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Survivability and Firepower Analysis Section, Ballistic Research Division, 

Ground Systems Research Center

ATTN: Masayuki Sakamoto 

2-9-54, Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa-ken 252-0206, 

JAPAN

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14. ABSTRACT

This report was written by the author under the Engineer Scientist Exchange Program activity in the US Army Research 

Laboratory from April 2013 to September 2014. To clarify the accuracy of finite element (FE) material models for butyl 

rubber, the component-level loading test was conducted on drop testers in various loading conditions. The test results are 

compared with the Finite Element Analysis (FEA) results of each FE-material model, and the errors in each material model 

are discussed on various metrics.

15. SUBJECT TERMS

ESEP, Blast-mitigating floor mat, Viscoelastic material, LS-DYNA

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Robert G Kargus

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iii

Contents

List of Figures iv

List of Tables v

Acknowledgments vi

1. Introduction 1

2. Experiment and Analysis Methods 1

2.1 Butyl Rubber........................................................................................................................ 1

2.2 Component Loading Test....................................................................................................2

2.3 Measurement........................................................................................................................ 4

2.4 Finite Element Analysis...................................................................................................... 6

3. Results and Discussion 11

3.1 Experimental Results......................................................................................................... 11

3.2 Comparison in Stress and Strain Histories.......................................................................14

3.3 Comparison in Stress–Strain Curves................................................................................18

4. Conclusions 24

5. References and Notes 25

6. List of Symbols, Abbreviations, and Acronyms 26

Distribution List 27
iv

List of Figures

Fig. 1 Test specimen of the butyl rubber ......................................................................................2

Fig. 2 Front view of the finger-crusher test rig on the loading table of the drop tester 

equipped with a specimen and sensors..........................................................................................2

Fig. 3 Dimensions of the finger-crusher test rig...........................................................................3

Fig. 4 Arrangements of sensors in the test setup..........................................................................5

Fig. 5 FE model of the component loading test ...........................................................................6

Fig. 6 Strain-rate-dependent loading–unloading curves for the ARL model .............................9

Fig. 7 Schematic of boundary conditions in FEAs ......................................................................9

Fig. 8 Velocity histories on the loading table in FEAs for 4-millisecond (msec) pulse 

loading........................................................................................................................................... 10

Fig. 9 Velocity histories on the loading table in FEAs for 8-msec-pulse loading ...................10

Fig. 10 Velocity histories on the loading table in FEAs for 20-msec-pulse loading .................11

Fig. 11 Typical load and deformation histories of the component loading test, X08_30_03 

(∆T = 8 msec, ∆V = 3.0 meters per second [m/s]).....................................................................12

Fig. 12 Example of the engineering stress history comparison between experiments and 

FEAs, X04_60 (∆T = 4 msec, ∆V = 6.0 m/s).............................................................................14

Fig. 13 Example of the engineering stress history comparison between experiments and 

FEAs, X08_60 (∆T = 8 msec, ∆V = 6.0 m/s).............................................................................15

Fig. 14 Example of the engineering stress history comparison between experiments and 

FEAs, X20_60 (∆T = 20 msec, ∆V = 6.0 m/s)...........................................................................15

Fig. 15 Example of the engineering strain history comparison between experiments and 

FEAs, X04_60 (∆T = 4 msec, ∆V = 6.0 m/s).............................................................................16

Fig. 16 Example of the engineering strain history comparison between experiments and 

FEAs, X08_60 (∆T = 8 msec, ∆V = 6.0 m/s).............................................................................16

Fig. 17 Example of the engineering strain history comparison between experiments and 

FEAs, X20_60 (∆T = 20 msec, ∆V = 6.0 m/s)...........................................................................17

Fig. 18 Peak stress errors of FEAs vs. experimental test data .....................................................18

Fig. 19 Impulse per unit cross-section errors of FEAs vs. experimental test data .....................18

Fig. 20 Peak strain errors of FEAs vs. experimental test data.....................................................18

Fig. 21 Example of the engineering stress–strain curve comparison between experiments 

and FEAs, X04_60 (∆T = 4 msec, ∆V = 6.0 m/s)......................................................................19

Fig. 22 Example of the engineering stress–strain curve comparison between experiments 

and FEAs, X08_60 (∆T = 8 msec, ∆V = 6.0 m/s)......................................................................19
v 

Fig. 23 Example of the engineering stress–strain curve comparison between experiments 

and FEAs, X20_60 (∆T = 20 msec, ∆V = 6.0 m/s)....................................................................20

Fig. 24 Schematic of the stress–strain curve and metrics............................................................21

Fig. 25 Initial modulus errors of FEAs versus experimental test data........................................22

Fig. 26 Loading modulus errors of FEAs versus experimental test data ....................................22

Fig. 27 Encircled area errors of FEAs versus experimental data. (LSTC model’s errors are 

omitted due to poor differentiation in the loading–unloading curves.).....................................22

Fig. 28 Strain-rate histories of the specimen in the test condition, X04_60 (∆T = 4 msec, 

∆V = 6.0 m/s)................................................................................................................................ 23

List of Tables

Table 1 Loading conditions for the component loading test ..........................................................4

Table 2 Specifications of sensors used in the component loading test..........................................5

Table 3 FE-material models for the test rig’s parts.........................................................................6

Table 4 FE-material models for the butyl-rubber specimen part ...................................................7

Table 5 LS-DYNA material card for the LSTC model ..................................................................7

Table 6 LS-DYNA material card for the Humanetics model.........................................................8

Table 7 LS-DYNA material card for the ARL model ....................................................................8

Table 8 Summary of experimental results.....................................................................................13
vi

Acknowledgments

This report was written by the author under the Engineer Scientist Exchange Program activity in 

the US Army Research Laboratory (ARL) from April 2013 to September 2014. I would like to 

take this opportunity to thank the ARL for giving me the chance to learn and investigate blastloading issues in the state-of-the-art research environment. I also would like to thank the 

members of the Blast Protection Branch and its specialists for supporting the numerical analysis, 

experiment, data processing, and various discussions that gave me valuable ideas.
1 

1. Introduction 

Lower leg injury is a major injury mode induced by underbody blast loading associated with

improvised explosive device (IED) attacks against ground fighting vehicles.

1–4 Blast-mitigating 

floor mats are regarded as an effective countermeasure for injury prevention,

5,6 and the

methodology for their selection and optimization is in immediate need. However, the loading 

mechanics in the lower leg with the existence of the floor mat are not fully understood. Thus, we 

decided to clarify the mechanics through the Finite Element Analysis (FEA). In this approach, 

we selected the combination of the Hybrid III 50th Percentile anthropomorphic test device’s 

(ATD’s) lower leg and the butyl-rubber floor mat with their well-known characteristics. 

There are several finite element (FE) material models for the butyl rubber, and it is necessary to 

determine which model is to be used in the FEA. In this report, we present the accuracy of FEmaterial models for the butyl rubber through the comparison between the FEA and component 

loading test. 

2. Experiment and Analysis Methods 

2.1 Butyl Rubber

The butyl rubber used in this study was manufactured by Humanetics Innovative Solutions. This 

is the same material used in the neck components of the Hybrid III 50th Percentile ATD. The

dimensions of a bulk sheet were 8 inches × 8 inches × 20 millimeters (mm), and test specimens 

were cut off from the sheet in the shape of cylinders (φ3 inches × 20 mm) as shown in Fig. 1. 

Before the component loading test was conducted, each specimen received compression loading 

up to 40% deformation against its thickness. This preloading process was intended to initialize 

the material status considering the Mullins effect, and neither permanent deformation nor 

fracture occurred on the specimens during this process. 
2 

Fig. 1 Test specimen of the butyl rubber

2.2 Component Loading Test 

The component loading test was conducted on the drop tester with the finger-crusher test rig in 

Fig. 2. The dimensions of the test rig are shown in Fig. 3. In this test setup, the lower plate, load 

cell, and base were rigidly assembled and fixed on the loading table of the drop tester. Thus, the 

specimen was compressed between the plates in the drop impact, and the material’s behavior was

known from the applied load and displacement between the plates. 

The test was conducted on the drop testers (Lansmont, P65 and P45) at the Adelphi Laboratory 

Center, U.S. Army Research Laboratory (ARL), at room temperature. The loading conditions in 

the test are listed in Table 1. Test specimens were reused several times after the confirmation of 

the material’s condition, and the interval between each test was kept to more than an hour for the 

material’s relaxation. 

Fig. 2 Front view of the finger-crusher test rig on the loading table of the

drop tester equipped with a specimen and sensors
3 

Fig. 3 Dimensions of the finger-crusher test rig

Front View Side View

Top View

Specimen

φ76Xh20

(Dimensions: mm)

381

254

Upper

Plate

Lower

Plate

Load Cell

φ102Xh25

Base

Plate

254

51 25

254

25

Mass (Upper Plate): 8.97kg

Mass (Lower Plate): 4.48kg

Bolted:

Lower Plate / Load Cell Interface

Load Cell / Base Plate Interface
4 

Table 1 Loading conditions for the component loading test

2.3 Measurement

The arrangements of sensors in the test setup are shown in Fig. 4, and the specifications are listed

in Table 2. The signals from sensors were recorded in the data acquisition system (Spectral 

Dynamics, SYSCHASVXI-5) at the sampling frequency of 250 kHz. Moreover, direct-current

offset and a CFC1000 filter were applied to each signal in the postprocessing on the dataanalysis software (MathWorks, MATLAB). The test was also recorded by the high-speed

imaging camera (Phantom, Miro) for the confirmation of the specimen’s behavior and the test 

rig’s rigidity. 
5 

Fig. 4 Arrangements of sensors in the test setup

Table 2 Specifications of sensors used in the component loading test

The input acceleration used to calculate ∆V on the loading table was the average of the outputs

from 2 accelerometers (Loading Tables A and B). The load applied on the specimen Lm was 

calculated from the output from the load cell L considering the inertial effect of the lower plate, 

as follows: 

Loading Table

Lower Plate

Upper Plate

Specimen

Base Plate

Accelerometer

(Loading Table B)

Accelerometer

(Upper Plate)

Potentiometer

(Upper Plate

-Base Plate)

Accelerometer

(Loading Table A)

Accelerometer

(Lower Plate)

Load Cell

(Lower Plate

– Base Plate)
6 

LLmm = LL − mmll × aall, (1)

where ml is the lower plate’s mass, and al is the acceleration on the lower plate.

2.4 Finite Element Analysis

There are 3 FE-material models for the butyl rubber fabricated on LS-DYNA simulation 

software by different developers: Livermore Software Technology Corp. (LSTC), Humanetics, 

and the ARL. In this study, we evaluated the accuracy of these models by comparing their FEA 

results with those of experiments with the finger-crusher test rig. Therefore, the FE model of the 

component loading test was built on LS-DYNA (Fig. 5) using material models listed in Table 3 

for the test rig’s parts. 

Fig. 5 FE model of the component loading test 

Table 3 FE-material models for the test rig’s parts

Front View

Number of Elements: 58904 Mesh Size (Specimen): 2.5mm

Iso View
7 

Three FE material models listed in Table 4 were used for the specimen part to make 

corresponding FE models. The LSTC material model and Humanetics material model are

derived from the neck component of the Hybrid III 50th ATD FEA models developed by LSTC 

and Humanetics.7,8 Both models are derivative of a viscoelastic material model, and the LSTC 

model is the most simplified description.

9 In addition to viscoelasticity, the Humanetics model 

contains Ogden hyperelasticity for the equilibrium part.

10

Table 4 FE-material models for the butyl-rubber specimen part

The LS-DYNA material cards used for the LSTC and Humanetics models are listed in Tables 5 

and 6. By contrast, the ARL model is a form-type model and refers to loading–unloading curves 

for its response considering strain-rate dependency.11 The material card of the ARL model is 

listed in Table 7. 

Table 5 LS-DYNA material card for the LSTC model
8 

Table 6 LS-DYNA material card for the Humanetics model

Table 7 LS-DYNA material card for the ARL model

The ARL model’s loading–unloading curves are developed through the dynamic loading test 

developed at Purdue University as shown in Fig. 6.

RO=1.700e-6 (kg/mm3

)

PR=0.49

MU1=8.100e-004 (GPa)

MU2=7.220e-005 (GPa)

MU3=-9.710e-005 (GPa)

ALPHA1=1.3

ALPHA2=4.0

ALPHA3=-2.0

GI=3.200E-2 (GPa)

BETAI=1.600 (GPa)

Parameters

RO=1.600e-6 (kg/mm3

)

K=2.900 (GPa)

MU=0.900 (GPa)

G=0.100 (GPa)

SIGF=1.000e-4 (GPa)

Parameters
9 

Fig. 6 Strain-rate-dependent loading–unloading curves

for the ARL model

Each FE model was applied the same boundary conditions as shown in Fig. 7 according to the 

acceleration histories on the loading table in experiments. Thus, the velocity histories in Fig. 8–

10 were generated on FE models as the loading conditions. 

Fig. 7 Schematic of boundary conditions in FEAs

-25

-20

-15

-10

-5

0

5

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Stress (MPa)

Strain

Loading (160/s)

Loading (10/s)

Loading (1/s)

Loading (0.1/s)

Loading (0.01/s)

Unloading

Gravity Initial Velocity

Velocity Change
10

Fig. 8 Velocity histories on the loading table in FEAs

for 4-millisecond (msec) pulse loading

Fig. 9 Velocity histories on the loading table in FEAs

for 8-msec-pulse loading

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

0 5 10 15 20 25 30

Velocity (m/s)

Time (msec)

X04_30

X04_45

X04_60

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

0 5 10 15 20 25 30

Velocity (m/s)

Time (msec)

X08_30

X08_45

X08_60
11

Fig. 10 Velocity histories on the loading table in FEAs

for 20-msec-pulse loading 

3. Results and Discussion 

3.1 Experimental Results

Typical load and deformation histories of the component loading test are shown in Fig. 11. There 

is a delay in the deformation response most likely due to the viscoelastic behavior of the butyl 

rubber. The experimental results are summarized in Table 8. 

The deviation of the results in each loading condition is less than 10% except for the deformation 

peak in 20-msec-pulse loading, and these are believed to be small enough to compare the results 

with those of FEAs. Considering the accuracy of the potentiometer (Celesco MT2A-30E-33, 

0.15% of full scale), it seems that the small deformations in 20-msec-pulse loading were not 

measured precisely. Therefore, the reliability of these results is lower than that of others. This 

should be considered in the following discussion. 

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

0 5 10 15 20 25 30

Velocity (m/s)

Time (msec)

X20_30

X20_45

X20_60
12

Fig. 11 Typical load and deformation histories of the component loading test, 

X08_30_03 (∆T = 8 msec, ∆V = 3.0 meters per second [m/s]) 

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30

Deformation (mm)

Load (kN)

Time (msec)

Load

Deformation
13

Table 8 Summary of experimental results

X04_30_01 4.7 3.0 13.3 31.1 3.36

Shot

Code

Pulse

Duration,

∆T (msec)

Loading

Table

Velocity

Change,

∆V (m/s)

Peak

Deformation

(mm)

Peak

Load

(kN)

Applied

Impulse

(kN msec)

X04_30_03 4.2 3.0 13.4 31.7 3.14

X04_30_02 4.5 3.0 13.9 32.1 3.25

X04_45_01 3.9 4.4 22.7 4.87

Avg. / SD 4.5 / 6% 3.0 / 0% 13.5 / 2% 31.6 / 2% 3.25 / 3%

X04_45_03 3.9 4.4 22.6 46.3 5.09

47.3

X04_45_02 3.7 4.4 23.6 47.6 4.92

X04_60_01 3.3 6.0 35.3 5.73

Avg. / SD 3.8 / 3% 4.4 / 0% 23.0 / 2% 47.1 / 1% 4.96 / 2%

62.4

X04_60_02 3.3 5.9 36.2 62.7 6.22

Avg. / SD 3.3 / 2% 5.9 / 1% 35.8 / 1% 62.8 / 1% 6.08 / 5%

X04_60_03 3.2 5.9 35.9 63.2 6.28

29.7

X08_30_02 8.5 2.8 7.2 30.6 1.93

X08_30_01 8.3 2.9 7.4 1.73

11.3

Avg. / SD 8.6 / 4% 2.9 / 3% 7.5 / 3% 30.2 / 2% 1.93 / 9%

45.0

X08_30_03 9.0 3.0 7.7 30.4 2.12

X08_45_02 8.6 4.4 11.1 44.3 2.85

Avg. / SD 8.3 / 4% 4.4 / 0% 11.2 / 1% 44.7 / 1% 2.76 / 3%

X08_45_03 8.0 4.4 11.2 44.7 2.66

X08_45_01 8.4 4.4 2.77

59.4

X08_60_02 8.0 5.9 15.5 58.6 3.97

X08_60_01 7.9 5.9 16.1 4.01

2.6

Avg. / SD 8.0 / 1% 5.9 / 1% 15.9 / 2% 59.0 / 1% 3.91 / 4%

32.3

X08_60_03 8.0 6.0 16.1 59.2 3.74

X20_30_02 21.7 3.3 2.6 32.3 0.63

Avg. / SD 21.7 / 1% 3.4 / 3% 2.6 / 2% 31.5 / 4% 0.69 / 13%

X20_30_03 21.5 3.3 2.5 30.0 0.64

X20_30_01 21.9 3.5 0.79

45.1 / 2%

62.0

X20_45_03 21.2 4.8 4.2 45.4 1.26

44.2

X20_45_02 19.9 4.7 4.1 45.8 0.60

X20_45_01 20.7 4.6 4.1 0.62

X20_60_01 19.9 6.5 6.4 1.77

Avg. / SD 20.6 / 3% 4.7 / 2% 4.1 / 1% 0.83 / 45%

Avg. / SD 19.4 / 2% 6.5 / 1% 6.5 / 5% 61.4 / 1% 1.87 / 7%

X20_60_03 19.0 6.5 6.2 60.6 2.03

X20_60_02 19.3 6.6 6.8 61.6 1.81
14

3.2 Comparison in Stress and Strain Histories

The load and deformation histories of each experiment were transferred to the engineering stress 

and engineering strain histories according to the measured dimensions of the specimen. The 

stress and strain histories are shown in Figs. 12–17 with corresponding FEA results of each 

material model. The FEA results of the Humanetics model and ARL model agree with the 

experimental results in most of the loading conditions including delays in strain histories. 

Fig. 12 Example of the engineering stress history

comparison between experiments and FEAs,

X04_60 (∆T = 4 msec, ∆V = 6.0 m/s) 

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0 5 10 15 20 25 30

Engineering Stress (MPa)

Time (msec)

Experiment(X04_60_01)

Experiment(X04_60_02)

Experiment(X04_60_03)

FEA(LSTC)

FEA(HUMANETICS)

FEA(ARL)
15

Fig. 13 Example of the engineering stress history

comparison between experiments and FEAs,

X08_60 (∆T = 8 msec, ∆V = 6.0 m/s) 

However, the FEA results of the LSTC model significantly overshoot the experimental results in 

several loading conditions. Moreover, the LSTC model shows unrealistic double-curved 

response in 20-msec-pulse loading as shown in Fig. 14 and 17.

Fig. 14 Example of the engineering stress history

comparison between experiments and FEAs,

X20_60 (∆T = 20 msec, ∆V = 6.0 m/s) 

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 5 10 15 20 25 30

Engineering Stress (MPa)

Time (msec)

Experiment(X08_60_01)

Experiment(X08_60_02)

Experiment(X08_60_03)

FEA(LSTC)

FEA(HUMANETICS)

FEA(ARL)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20 25 30

Engineering Stress (MPa)

Time (msec)

Experiment(X20_60_01)

Experiment(X20_60_02)

Experiment(X20_60_03)

FEA(LSTC)

FEA(HUMANETICS)

FEA(ARL)
16

Fig. 15 Example of the engineering strain history comparison 

between experiments and FEAs, X04_60 

(∆T = 4 msec, ∆V = 6.0 m/s) 

Fig. 16 Example of the engineering strain history comparison 

between experiments and FEAs, X08_60 

(∆T = 8 msec, ∆V = 6.0 m/s) 

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 5 10 15 20 25 30

Engineering Strain

Time (msec)

Experiment(X04_60_01)

Experiment(X04_60_02)

Experiment(X04_60_03)

FEA(LSTC)

FEA(HUMANETICS)

FEA(ARL)

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0 5 10 15 20 25 30

Engineering Strain

Time (msec)

Experiment(X08_60_01)

Experiment(X08_60_02)

Experiment(X08_60_03)

FEA(LSTC)

FEA(HUMANETICS)

FEA(ARL)
17

Fig. 17 Example of the engineering strain history comparison 

between experiments and FEAs, X20_60 

(∆T = 20 msec, ∆V = 6.0 m/s) 

To clarify the accuracy of each material model, the errors of the FEA results versus the 

experimental results were compared for the peak stress, impulse per unit cross-section, and peak 

strain in Figs. 18–20. Thus, the errors probably have some relationships with the pulse durations 

because the tendencies are similar among loading conditions with the same pulse duration. 

Therefore, we will discuss the accuracy of material models mainly from this point of view.

The errors of the Humanetics model and the ARL model are less than 25% except for the strain 

errors in 20-msec-pulse loading, although the LSTC model has considerably larger errors. The 

strain errors in 20-msec-pulse loading are still large after considering the low reliability of the 

deformation measurement; the deviation in strain histories in the unloading phase of 20-msecpulse loading is also large (Fig.17). Because of the characteristic of viscoelastic material models, 

the Humanetics model assumes the same behavior for the loading–unloading phases; the ARL 

model considers only one curve for the unloading phase regardless of strain rate (as was shown 

in Fig. 6). Consequently, the unloading phases of each model contain larger errors than those of 

the loading phases (Fig. 20). Together with the long pulse duration, this probably leads to the 

accumulation of strain errors in 20-msec-pulse loading.

For these reasons, both the Humanetics model and ARL model can be used for the prediction of 

stress and strain histories, and also for that of impulse transfer in 4- and 8-msec-pulse loading. 

However, they require cautious use in longer-duration pulse loading.

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0 5 10 15 20 25 30

Engineering Strain

Time (msec)

Experiment(X20_60_01)

Experiment(X20_60_02)

Experiment(X20_60_03)

FEA(LSTC)

FEA(HUMANETICS)

FEA(ARL)
18

Fig. 18 Peak stress errors of FEAs vs. experimental test data

Fig. 19 Impulse per unit cross-section errors of FEAs vs. experimental test data

Fig. 20 Peak strain errors of FEAs vs. experimental test data

3.3 Comparison in Stress–Strain Curves

The stress and strain histories of each experiment were combined into stress–strain curves. The 

curves are shown in Figs. 21–23 with corresponding FEA results of each material model. The 

stress–strain curves in the experimental results show different paths for the loading–unloading 

phases and form encircled areas. The FEA results of the Humanetics model and ARL model 

agree with the experimental results in the formation of these encircled areas. By contrast, the 

-50%

-25%

0%

25%

50%

75%

X04_30 X04_45 X04_60 X08_30 X08_45 X08_60 X20_30 X20_45 X20_60

LSTC Humanetics ARL Experiment SD

-25%

0%

25%

50%

75%

X04_30 X04_45 X04_60 X08_30 X08_45 X08_60 X20_30 X20_45 X20_60

LSTC Humanetics ARL Experiment SD

-25%

0%

25%

50%

75%

100%

125%

150%

175%

X04_30 X04_45 X04_60 X08_30 X08_45 X08_60 X20_30 X20_45 X20_60

LSTC Humanetics ARL Experiment SD
19

FEA results of the LSTC model show almost identical paths for the loading–unloading phases in

4- and 8-msec-pulse loading, as shown in Figs. 21 and 22. 

Fig. 21 Example of the engineering stress–strain curve

comparison between experiments and FEAs,

X04_60 (∆T = 4 msec, ∆V = 6.0 m/s) 

Fig. 22 Example of the engineering stress–strain curve

comparison between experiments and FEAs,

X08_60 (∆T = 8 msec, ∆V = 6.0 m/s) 

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

-0.20 0.00 0.20 0.40 0.60

Engineering Stress (MPa)

Engineering Strain

Experiment(X04_60_01)

Experiment(X04_60_02)

Experiment(X04_60_03)

FEA(LSTC)

FEA(HUMANETICS)

FEA(ARL)

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

-0.10 0.00 0.10 0.20 0.30

Engineering Stress (MPa)

Engineering Strain

Experiment(X08_60_01)

Experiment(X08_60_02)

Experiment(X08_60_03)

FEA(LSTC)

FEA(HUMANETICS)

FEA(ARL)
20

Fig. 23 Example of the engineering stress–strain curve

comparison between experiments and FEAs,

X20_60 (∆T = 20 msec, ∆V = 6.0 m/s) 

There are 2 cases for the formation of encircled areas in FEAs: 

1) The material model assumes different material behaviors for the loading–unloading phases. 

However, the LSTC model is a viscoelastic material model and assumes the same behavior. 

2) The material model assumes different material behaviors for the deformation speeds, and 

the speeds are different in the loading–unloading phases. This is the case for the LSTC 

model, and will be discussed in this section. 

The shear relaxation modulus G(t) is defined in the LSTC model as follows:

GG(tt) = GG∞ + (GG0 − GG∞) ee−ββββ, (2) 

where GG∞is the infinite shear modulus, GG0 is the short-time shear modulus, and ββ is the decay 

constant. (GG∞, GG0 and ββ correspond to the parameters G0, GI, and BETA in Table 5, 

respectively.) 

Therefore, the sensitivity of the material behavior against deformation speed is governed by ββ in 

an exponential manner. Judging from the formation of the encircled area in Fig. 23, the LSTC 

model was probably tailored for the loading with pulse longer than 20 msec. Consequently, the 

sensitivity in 4- and 8-msec-pulse loading is not enough to differentiate the loading–unloading 

curves according to their differences in the deformation speeds. 

Although the Humanetics model has a similar description for the relaxation modulus as the 

LSTC model, the loading–unloading curves are differentiated. Moreover, the ARL model also 

differentiates the loading–unloading curves. Therefore, the Humanetics model and ARL model 

can be used for the evaluation of these loading–unloading events. 

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-0.05 0.00 0.05 0.10 0.15

Engineering Stress (MPa)

Engineering Strain

Experiment(X20_60_01)

Experiment(X20_60_02)

Experiment(X20_60_03)

FEA(LSTC)

FEA(HUMANETICS)

FEA(ARL)
21

To clarify the accuracy of each material model, several metrics, E0, ELoad, and Sss, are

implemented as shown in Fig. 24. Each metric is defined below. 

Fig. 24 Schematic of the stress–strain curve and metrics

The initial modulus E0 represents the instantaneous material behavior and is defined as follows: 

EE0 = σσ0−0

0.005−0 , (5) 

where σ0 is the stress at 0.5% strain.

The loading modulus ELoad represents the overall loading behavior and is defined as follows:

EELLLLLLLL = σσMMMMMM−0

εεPP−0 , (6) 

where σMAX is the maximum stress, and εP is the strain at the maximum stress point.

Encircled area Sss represents the absorbed energy during the loading–unloading event and is 

defined as follows:

SSSSSS = ∫ (σσ′ εεMMMMMM

0 − σσ")dddd , (7) 

where σ’ is the stress in the loading curve, σ” is the stress in the unloading curve, and εMAX is 

the maximum strain.

The errors of the FEA results versus the experimental results were calculated in these 3 metrics, 

as shown in Figs. 25–27. The errors of E0 show that all 3 material models are not suitable for the 

prediction of instantaneous material behavior such as the rising edges of the experimental results 

(in Figs. 21 and 22). 

Stress, σ

Strain, ε

0

Sss

ε=0.5% ε=εMAX

σ=σMAX

E0

ELoad

ε=εP

σ=σQ

σ=σ0

σ’

σ’’
22

Fig. 25 Initial modulus errors of FEAs versus experimental test data

Fig. 26 Loading modulus errors of FEAs versus experimental test data

Fig. 27 Encircled area errors of FEAs versus experimental data. (LSTC model’s errors are omitted due 

to poor differentiation in the loading–unloading curves.) 

As shown in Fig. 26, the errors of ELoad are less than 25% in most of the FEA results of the ARL 

model in 4- and 8-msec-pulse loading. The only exception is the loading condition X04_60; this 

has the highest strain rate due to its short-duration, high-amplitude pulse. The strain rates of the 

experimental results in this loading condition are shown in Fig. 28. The maximum strain rate is 

approximately 150/s, and this is lower than the upper limit of the strain rate defined in the 

loading curves of the ARL model as shown in Fig. 6 (160/s). However, the strain rate in Fig. 28 

-100%

-75%

-50%

-25%

0%

25%

50%

X04_30 X04_45 X04_60 X08_30 X08_45 X08_60 X20_30 X20_45 X20_60

LSTC Humanetics ARL Experiment SD

-75%

-50%

-25%

0%

25%

50%

75%

X04_30 X04_45 X04_60 X08_30 X08_45 X08_60 X20_30 X20_45 X20_60

LSTC Humanetics ARL Experiment SD

-100%

0%

100%

200%

300%

X04_30 X04_45 X04_60 X08_30 X08_45 X08_60 X20_30 X20_45 X20_60

Humanetics ARL Experiment SD
23

is the averaged value over the whole specimen. Therefore, the partial strain rate probably 

exceeds the upper limit, and the ARL model tends to underestimate ELoad as E0 in this loading 

condition. Moreover, this also leads to the underestimation of peak stress in the loading condition 

X04_60 as shown in Fig. 18. The FEA results of the Humanetics model and LSTC model also 

show small errors of ELoad in several loading conditions, but the errors are generally larger than 

those of the ARL model. 

Fig. 28 Strain-rate histories of the specimen in the test

condition, X04_60 (∆T = 4 msec, ∆V = 6.0 m/s) 

As to Sss, the Humanetics model and ARL model show small errors for 4- and 8-msec-pulse 

loading. However, the deviation is larger than that of E0; this should be noted in the evaluation 

of energy absorption on the FEA. In 20-msec-pulse loading, both models show large errors due 

to the overestimated strain in the unloading phase, which was discussed previously. 

For these reasons, both the Humanetics model and ARL model can be used for the prediction of 

stress–strain curves in 4- and 8-msec-pulse loading, whereas the instantaneous material 

behaviors are not completely simulated. Both models also can be used for the prediction of 

energy absorption with larger errors. Moreover, the ARL model is superior to the Humanetics 

model, especially in the prediction of loading behavior.

-200.00

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

5.0 7.5 10.0 12.5

Strain Rate (1/sec)

Time (msec)

X04_60_01

X04_60_02

X04_60_03
24

4. Conclusions 

In this study, we conducted component loading tests of butyl rubber and compared the results 

with those of FEAs to clarify the accuracy of the FE-material models. The Humanetics model 

and ARL model showed good accuracy in 4- and 8-msec-pulse loading for the prediction of 

stress history, strain history, stress–strain curve, impulse transfer, and energy absorption, while 

the LSTC model showed significant errors. Moreover, the ARL model is superior to the 

Humanetics model especially with its higher accuracy in the loading phase. Therefore, we 

conclude that the ARL model is to be used in the forthcoming FEA of the ATD’s lower leg and 

the butyl-rubber floor mat. However, the current ARL model has two problems to be corrected: 

1) The strain-rate dependency in the unloading phase is not completely installed in the 

models. This leads to the excessive recovery delay, especially in long-duration pulse 

loading.

2) The strain-rate dependency shown in Fig. 6 does not cover the partial, high strain-rate 

deformation. This leads to the excessively soft behavior in the loading phase and 

underestimation of the maximum stress. 

Problem 2, in particular, affects the 4-msec-pulse loading that we frequently use in the evaluation 

of underbody blast-loading events. Therefore, the ARL model’s improvement is strongly 

recommended.
25

5. References and Notes

1. Dougherty AL, Mohrle CR, Galarneau MR, Woodruff SI, Dye JL, Quinn KH. Battlefield 

extremity injuries in Operation Iraqi Freedom. Injury. 2009;40(7):772–777. 

2. Belmont PJ, Schoenfeld AJ, Goodman G. Epidemiology of combat wounds in Operation 

Iraqi Freedom and Operation Enduring Freedom: orthopaedic burden of disease. J Surg 

Orthop Adv. 2010;19(1):2–7. 

3. Eskridge SL, Macera CA, Galarneau MR, Holbrook TL, Woodruff SI, MacGregor AJ, 

Morton DJ, Shaffer RA. Injuries from combat explosions in Iraq: injury type, location, and 

severity. Injury. 2012;43(10):1678–1682. 

4. Test methodology for protection of vehicle occupants against anti-vehicular landmine 

effects. NATO; 2007. Report No.: TR-HFM-090. 

5. Golan G, Asaf Z, Ran E, Aizik F. Occupant legs survivability: an assessment through the 

utilization of field blast test methodology. Paper presented at: MABS22. Proceedings of the 

22nd International Symposium on Military Aspects of Blast and Shock; 2012 Nov 4–9; 

Bourges, France. 

6. Dong L, Zhu F, Jin X, Suresh M, Jiang B, Sevagan G, Cai Y, Li G, Yang KH. Blast effect on 

the lower extremities and its mitigation: a computational study. J Mech Behav Biomed 

Mater. 2013;28:111–124. 

7. Livermore Software Technology Corp. National Crash Analysis Center, Hybrid III 50th

Percentile Dummy, model LSTC. 

8. Humanetics Innovative Solutions, Hybrid-III 50th Percentile Male Dummy, model v7.0. 

9. Livermore Software Technology Corp. (US). LS-DYNA Keyword User’s Manual–Volume 

III Material Models (Rev. 3372). 2013. p. 3–78, 79.

10. Effinger V. Modeling of viscoelastic materials with LS-DYNA. Paper presented at: 11th

German LS-DYNA Forum. Proceedings of NAFEMS Conference; 2012 Oct 9–10; Ulm, 

Germany. p. 11,15,17. 

11. Kolling S, DuBois PA, Benson DJ. A simplified rubber model with damage. Paper presented 

at: 4th German LS-DYNA Forum. Proceedings of NAFEMS Conference; Bamberg,

Germany. 2005. p. B.II.1–10. 
26

6. List of Symbols, Abbreviations, and Acronyms

ARL US Army Research Laboratory

ATD anthropomorphic test device

FE Finite Element

FEA Finite Element Analysis

IED improvised explosive device

kN kilonewton

LSTC Livermore Software Technology Corporation

mm millimeter 

msec millisecond

m/s meters per second 
27

 1 DEFENSE TECH INFO CTR 

(PDF) ATTN DTIC OCA

 2 US ARMY RSRCH LABORATORY

(PDF) ATTN IMAL HRA MAIL & RECORDS MGMT

 ATTN RDRL CIO LL TECHL LIB

 1 US ARMY RSRCH LAB

(PDF) ATTN RDRL WMP F R KARGUS
28

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