Transfer Relation between the Compression Test Rig and 

the Anthropomorphic Test Device (ATD) Lower Leg

by Masayuki Sakamoto

ARL-SR-0330 August 2015 

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Army Research Laboratory

Adelphi, MD 20783-1138

ARL-SR-0330 August 2015 

Transfer Relation between the Compression Test Rig and 

the Anthropomorphic Test Device (ATD) Lower Leg

Masayuki Sakamoto

Japanese ESEP Research Engineer 

at Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution unlimited. 
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04/2014–09/2014 

4. TITLE AND SUBTITLE

Transfer Relation between the Compression Test Rig and the Anthropomorphic 

Test Device (ATD) Lower Leg

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Masayuki Sakamoto 

(Japanese Engineer Scientist Exchange Program Research Engineer) 

5d. PROJECT NUMBER

ESEP

5e. TASK NUMBER

5f. WORK UNIT NUMBER

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

US Army Research Laboratory

ATTN: RDRL-WMP-F 

2800 Powder Mill Road 

Adelphi, MD 20783-1138 

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9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

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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before publication, please forward this report to the Technical Research and Development Institute (TRDI), JMOD for 

approval to publish this report (JMOD/TRDI POC: Mr. Masayuki Sakamoto, Survivability and Firepower Analysis Section, 

Ballistic Research Division, Ground Systems Research Center [E-mail: masayuki@cs.trdi.mod.go.jp, Phone:+81-42-752-

2941, Address:2-9-54, Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa-ken 252-0206, JAPAN]). Retain a copy of the 

approval with the Form-1 record.

14. ABSTRACT

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

(ARL) from April 2013 to September 2014. We developed the Compression Test Rig (CTR) that is capable of evaluating the 

effectiveness of the blast-mitigating floor mat against assessed lower leg injury. The CTR was fabricated to simulate the 

loading status under the anthropomorphic test device (ATD) lower leg in the blast-loading event, and the transfer relation 

between the CTR response and ATD lower-leg response was clarified through the drop test with various loading conditions. 

15. SUBJECT TERMS

ESEP, blast-mitigating floor mat, Evaluation methodology, Drop test 

16. SECURITY CLASSIFICATION OF:

17. LIMITATION

 OF 

 ABSTRACT

UU

18. NUMBER

 OF 

 PAGES

34 

19a. NAME OF RESPONSIBLE PERSON

Robert G Kargus

a. REPORT

Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

Unclassified

19b. TELEPHONE NUMBER (Include area code) 

(301) 394-5738

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18
iii

Contents

List of Figures iv

List of Tables v

Acknowledgments vi

1. Introduction 1

2. Material and Methods 1

2.1 Design of the CTR............................................................................................................... 1

2.2 Loading Test of the CTR and ATD Lower Leg ..............................................................10

3. Results and Discussion 13

3.1 Experimental Results......................................................................................................... 13

3.2 Development of Transfer Relation ...................................................................................14

3.2 Prediction of ATD Lower-Leg Response Based on the CTR Response........................20

4. Conclusions 23

5. References 24

List of Symbols, Abbreviations, and Acronyms 25

Distribution List 26
iv

List of Figures

Fig. 1 Conceptual drawing of the CTR.........................................................................................2

Fig. 2 Schematic of the response conversion between the CTR response and ATD lowerleg response..................................................................................................................................... 2

Fig. 3 FEA model for the ATD lower-leg loading.......................................................................3

Fig. 4 Typical pressure distribution under the boot sole in the FEA result................................4

Fig. 5 Load histories of the ATD lower leg in 10-meter-per-second (m/s), 10-millisecond 

(msec) pulse loading FEA.............................................................................................................. 4

Fig. 6 FEA model for the CTR loading ........................................................................................5

Fig. 7 Load histories of the ATD lower leg and CTR (4.8 kg) in 10-m/s, 2.5-msec-pulse 

loading FEA.................................................................................................................................... 5

Fig. 8 Load histories of the ATD lower leg and CTR (4.8 kg) in 10-m/s, 5.0-msec-pulse 

loading FEA.................................................................................................................................... 6

Fig. 9 Load histories of the ATD lower leg and CTR (4.8 kg) in 10-m/s, 10-msec-pulse 

loading FEA.................................................................................................................................... 6

Fig. 10 Relation between the peak load and pulse duration ..........................................................7

Fig. 11 Relation between the applied impulse and pulse duration................................................7

Fig. 12 Load histories of the ATD lower leg and CTR (1.3 kg) in 10-m/s, 2.5-msec-pulse 

loading FEA.................................................................................................................................... 8

Fig. 13 Load histories of the ATD lower leg and CTR (3.7 kg) in 10-m/s, 5-msec-pulse 

loading FEA.................................................................................................................................... 8

Fig. 14 Load histories of the ATD lower leg and CTR (6.6 kg) in 10-m/s, 10-msec-pulse 

loading FEA.................................................................................................................................... 9

Fig. 15 Drawings of the CTR prototype .......................................................................................10

Fig. 16 Arrangements of sensors in the test setup for the CTR loading .....................................12

Fig. 17 Arrangements of sensors in the test setup for the ATD lower-leg loading....................12

Fig. 18 Typical input- and output-acceleration histories in the CTR loading, CTR_03 

(Height = 30 inches)..................................................................................................................... 13

Fig. 19 Typical input-acceleration history and ATD lower-tibia load history in the ATD 

lower-leg loading, ATD_03 (Height = 30 inches) .....................................................................14

Fig. 20 Schematic of the transfer relation between the CTR response and ATD lower-leg 

response......................................................................................................................................... 15

Fig. 21 Synchronized crosshead-acceleration histories in the CTR loading ..............................15

Fig. 22 Synchronized lower-tibia load histories in the ATD lower-leg loading ........................16

Fig. 23 Relation between the ATD lower-tibia load and CTR crosshead acceleration in 
v 

each loading condition ................................................................................................................. 16

Fig. 24 Schematic of the amplitude–domain transfer relation between the CTR response 

and ATD lower-leg response ....................................................................................................... 17

Fig. 25 Relation between the duration and normalized response of the CTR loading ..............18

Fig. 26 Relation between the duration and normalized response in the ATD lower-leg 

loading........................................................................................................................................... 18

Fig. 27 Relation of the pulse duration between the ATD lower-tibia response and CTR 

crosshead response in each loading condition............................................................................19

Fig. 28 Schematic of the duration–domain transfer relation between the CTR response and 

ATD lower-leg response .............................................................................................................. 20

Fig. 29 Comparison between the ATD lower-leg experimental response and predictive 

response from the CTR response, CTR_02/ATD_02 (∆V = 4.86 m/s) ....................................21

Fig. 30 Comparison between the ATD lower-leg experimental response and predictive 

response from the CTR response, CTR_04/ATD_04 (∆V = 6.26 m/s) ....................................21

Fig. 31 Example of the application of the transfer relation to the butyl-rubber floor mat in 

the FEA, CTR_03/ATD_03 (∆V = 5.26 m/s).............................................................................22

List of Tables

Table 1 FE material models for the floor-mat and floor-plate parts..............................................3

Table 2 Specifications of the CTR...................................................................................................9

Table 3 Loading conditions for the CTR loading and ATD lower-leg loading ..........................11

Table 4 Specifications of sensors used in the CTR loading and ATD lower-leg loading..........13

Table 5 Average velocity changes in each loading condition ......................................................14

Table 6 Parameters for Eqs. 1 and 2 in each loading condition...................................................17

Table 7 Parameters for Eq. 3 in each loading condition...............................................................20

Table 8 FE-material models for the butyl rubber..........................................................................22

Table 9 Errors in the ATD lower-leg response prediction from the CTR response ...................23
vi

Acknowledgments

This report was written by the author under the Engineer Scientist Exchange Program 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 blast-loading 

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, experiments, 

data processing, and various discussions that gave me valuable ideas. I especially appreciate 

ARL researcher Robert G Kargus’s invitation for me to participate in the Underbody Blast 

Mitigation (UBM) program. This report was written in the collaborative research with him. Mr. 

Kargus invented the concept of the Compression Test Rig and energetically led its development 

and experimental verification. He also supported me in the writing and polishing of this report, 

for which I am sincerely grateful. 
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 It is also widely 

believed that blast-mitigating floor mats are effective means for reducing the severity of lower 

leg injury.

5–7 Until now, it has been necessary to conduct the loading test with the 

anthropomorphic test device (ATD) lower leg for evaluations at the US Army Research 

Laboratory (ARL). However, the loading test with the ATD lower leg is expensive and time

consuming; simplified methodology is in immediate need. 

Under the auspices of the Underbody Blast Mitigation (UBM) program, we will develop the 

simplified methodology for the evaluation of floor-mat effectiveness. In this study, we developed

the Compression Test Rig (CTR) that is capable of evaluating the mat’s effectiveness against

assessed lower leg injury. Firstly, we designed the CTR that represented the loading status under 

the ATD lower leg. Secondly, we conducted loading test of the nominal floor mat with the ATD 

lower leg and CTR. Then, we compared the responses to establish transfer relation between these 

2 test configurations and investigated the applicability of the CTR in the floor-mat evaluation

instead of the ATD lower leg.

2. Material and Methods 

2.1 Design of the CTR 

The CTR was designed as simple as possible to increase its availability to various stakeholders

for the evaluation of the floor mat. The concept drawing of the CTR is shown in Fig. 1. In the 

testing, the CTR is fixed on the loading table of the drop tester, and the floor mat is compressed 

by the inertia of the indenter and crosshead; this produces an input and output relationship from 

the acceleration of the table and crosshead. In the evaluation, the crosshead acceleration is

converted based on the transfer relation (Fig. 2) to the corresponding ATD lower-leg tibia load, 

which is a major criterion for the lower leg injury.
2 

Fig. 1 Conceptual drawing of the CTR 

Fig. 2 Schematic of the response conversion between the CTR response and ATD lower-leg response

To simplify the transfer relation, it is necessary to generate the same material behavior in the 

floor mat between the CTR loading and ATD lower-leg loading. Therefore, we conducted the 

preliminary Finite Element Analysis (FEA) to clarify the loading status using the FE model of 

Floor Mat

Indenter Crosshead

Drop Impact

Floor Plate

CTR Loading

Configuration

Floor Plate

Floor Mat

ATD Lower Leg Loading

Configuration

Crosshead

Indenter

Input Pulse 

on the Loading Table

of the Drop Tester

Transfer

Relation

Lower Tibia

Load Fz

Crosshead

Acceleration
3 

the ATD lower-leg loading, as seen in Fig. 3. The FE-material models used in the floor-mat and 

floor-plate parts are listed in Table 1.

Fig. 3 FEA model for the ATD lower-leg loading 

Table 1 FE material models for the floor-mat and floor-plate parts

The pressure distribution under the boot sole was clarified (Fig. 4). There are high-pressure areas 

under the toe and heel. The load histories of a representative FEA result are shown in Fig. 5. 

Then, the tendency of loading by the boot heel and lower tibia is similar, although the boot toe

shows different tendency. Therefore, it is convenient to generate similar loading status in the 

CTR loading as the boot-heel loading for the development of a simple transfer relation. 

Considering this, the cross-section of the CTR was determined to approximate the area of the 

boot heel. Moreover, the moving mass—indenter and crosshead—of the CTR was arranged 

temporarily as 4.8 kg (hereafter the fixed-mass CTR).

Input Pulse 

Hybrid III 50th

ATD Right Leg

Floor Mat

Floor Plate Boots
4 

Fig. 4 Typical pressure distribution under the boot sole in the FEA result

Fig. 5 Load histories of the ATD lower leg in 10-meter-per-second (m/s), 

10-millisecond (msec) pulse loading FEA

To confirm the loading status under this CTR indenter, FEAs were conducted in various loading 

conditions using the FE model, as illustrated in Fig. 6. The FE-material models used in this FE 

model were identical to those of the ATD lower-leg loading (Table 1). 

Toe

Heel

Stress

Low High

Pulse Loading
5 

Fig. 6 FEA model for the CTR loading 

The FEA results are shown in Figs. 7–9 with those of the ATD lower-leg loading. The loads 

applied by the CTR indenter differ from those applied by the boot heel. 

Fig. 7 Load histories of the ATD lower leg and CTR 

(4.8 kg) in 10-m/s, 2.5-msec-pulse loading FEA

CTR

Indenter

Floor Mat

Floor Plate CTR

Indenter

Floor Mat

Floor Plate

Input Pulse
6 

Fig. 8 Load histories of the ATD lower leg and CTR 

(4.8 kg) in 10-m/s, 5.0-msec-pulse loading FEA

Fig. 9 Load histories of the ATD lower leg and CTR

(4.8 kg) in 10-m/s, 10-msec-pulse loading FEA

To clarify this tendency, the peak loads and applied impulses are shown in Figs. 10 and 11. The 

fixed-mass CTR clearly shows a different loading tendency from the ATD lower leg, especially 

in the peak loads; thus we conclude that it is impossible to simulate the same loading condition 

as the boot heel with the fixed-mass CTR.

0

5

10

15

20

25

5 10 15 20

Load (kN)

Time (msec)

Lower Tibia

Boots Toe 

Boots Heel 

Whole Boots 

CTR

0

5

10

15

20

25

5 10 15 20

Load (kN)

Time (msec)

Lower Tibia

Boots Toe 

Boots Heel 

Whole Boots 

CTR
7 

Fig. 10 Relation between the peak load and pulse duration

Fig. 11 Relation between the applied impulse and pulse duration

Additional analyses were conducted with CTRs that had various masses to determine the 

adequate mass for each loading pulse—hereafter, the variable-mass CTR—as shown in Figs. 12–

14. (The FEA results are also summarized in Figs. 10 and 11.) Thus, there is agreement between 

the boot-heel loading and variable-mass CTR loading.

0.0

5.0

10.0

15.0

20.0

25.0

0.0 2.5 5.0 7.5 10.0 12.5

Peak Load (kN)

Pulse Duration (msec)

Boots Heel

CTR (Fixed-Mass)

CTR (Variable-Mass)

0.0

25.0

50.0

75.0

100.0

0.0 2.5 5.0 7.5 10.0 12.5

Applied Impulse (Nsec)

Pulse Duration (msec)

Boots Heel

CTR (Fixed-Mass)

CTR (Variable-Mass)
8 

Fig. 12 Load histories of the ATD lower leg and CTR 

(1.3 kg) in 10-m/s, 2.5-msec-pulse loading FEA

Fig. 13 Load histories of the ATD lower leg and CTR 

(3.7 kg) in 10-m/s, 5-msec-pulse loading FEA

0

5

10

15

20

25

5 10 15 20

Load (kN)

Time (msec)

Lower Tibia

Boots Toe 

Boots Heel 

Whole Boots 

CTR

0

5

10

15

20

25

5 10 15 20

Load (kN)

Time (msec)

Lower Tibia

Boots Toe 

Boots Heel 

Whole Boots 

CTR
9 

Fig. 14 Load histories of the ATD lower leg and CTR 

(6.6 kg) in 10-m/s, 10-msec-pulse loading FEA

In this study we focused on the 5-msec-pulse loading, which is one of the most frequent loading 

conditions in the evaluation of underbody blast loading. Therefore, the specifications of the CTR 

were determined (Table 2) by considering the relation between the CTR mass and response.

According to these specifications, the CTR was fabricated as shown in Fig. 15. 

Table 2 Specifications of the CTR

0

5

10

15

20

25

5 10 15 20

Load (kN)

Time (msec)

Lower Tibia

Boots Toe 

Boots Heel 

Whole Boots 

CTR

3.9

- Cylinder

(φ4"x0.5")

Target Design

3.7

9000 8200

Specification

Moving Mass

(Indenter+Crosshead)

(kg)

Indenter

Shape

Indenter

Cross-section

(mm2

) 
10

Fig. 15 Drawings of the CTR prototype

2.2 Loading Test of the CTR and ATD Lower Leg

To develop the transfer relation between the CTR and ATD lower leg, the loading test with

conditions in Table 3 were conducted in both test configurations. The responses of the CTR and 

ATD lower leg were measured in the crosshead acceleration and lower-tibia load, respectively. 

Moreover, SKYDEX material was used as the nominal floor mat in this loading test. 

Iso View

Front View
11

Table 3 Loading conditions for the CTR loading and ATD lower-leg loading 

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

Laboratory Center, ARL. The arrangements of sensors in both test setups are shown in Figs. 16 

and 17, and the specifications are listed in Table 4. 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 the filters (Table 4) were applied to each signal in 

post-processing with the data-analysis software (MathWorks, MATLAB). The test was also 

recorded by the high-speed imaging camera (Phantom, Miro) for the confirmation of the test 

rig’s behavior. 
12

Fig. 16 Arrangements of sensors in the test setup for the CTR loading

Fig. 17 Arrangements of sensors in the test setup for the ATD lower-leg loading 

Accelerometer

(Input)

Loading Table

Floor Plate

Floor Mat

Crosshead

Indenter

Accelerometer

(Output)

Floor Plate

Floor Mat

Accelerometer

(Input)

Hybrid III 50th

ATD Left Leg

Boots

Lower Tibia

Load Cell

Loading Table
13

Table 4 Specifications of sensors used in the CTR loading and ATD lower-leg loading 

3. Results and Discussion 

3.1 Experimental Results

The typical responses of the CTR and ATD lower leg are shown in Figs. 18 and 19. The velocity 

change of each loading condition is summarized in Table 5. The responses show different delays 

in the peak value against the input pulses. Both responses have longer-duration pulses than their 

input-acceleration pulses, and the ATD lower leg shows longer-duration responses than the CTR. 

Moreover, there are plateau regions (second peaks) on the loading phase of the ATD lower-leg 

response, although the corresponding clues are not clear in the CTR response. These plateau 

regions were possibly generated as the results of the shock mitigation in the ATD foot flesh and

boot sole and the floor mat. 

Fig. 18 Typical input- and output-acceleration

histories in the CTR loading, CTR_03 

(Height = 30 inches) 

0

1000

2000

3000

-2 0 2 4 6 8 10 12 14

Acceleration (kN)

Time (msec)

Input Acceleration

Output Acceleration
14

Fig. 19 Typical input-acceleration history and ATD

lower-tibia load history in the ATD lower-leg

loading, ATD_03 (Height = 30 inches) 

Table 5 Average velocity changes in each loading condition 

3.2 Development of Transfer Relation

The concept of the transfer relation developed in this study is shown in Fig. 20.

8 In this concept, 

the transfer relations were developed in the acceleration–force (amplitude–domain) transfer and 

time–time (duration–domain) transfer independently. To develop these transfer relations, it was 

necessary to compare the responses of the CTR and ATD lower leg in the amplitude domain and 

duration domain at each loading condition. 

0.0

2.5

5.0

7.5

0

1000

2000

3000

-2 0 2 4 6 8 10 12 14

Load (kN)

Acceleration (kN)

Time (msec)

Input Acceleration

Lower Tibia Load
15

Fig. 20 Schematic of the transfer relation between the CTR response and ATD lower-leg response

In the amplitude–domain comparison, the responses of the CTR and ATD lower leg were 

synchronized by setting their peaks to the time zero as shown in Figs. 21 and 22. Then, the 

responses of both test configurations were related in the amplitude domain as shown in Fig. 23. 

Fig. 21 Synchronized crosshead-acceleration histories

in the CTR loading

Acceleration 

Time Time Load

Input Output Acceleration-Force Input Output

(Amplitude-Domain) 

Transfer

Time-Time

(Duration-Domain)

Transfer

CTR ATD Lower Leg

0

2500

5000

7500

-10 -5 0 5 10

Acceleration (m/s2)

Time(msec)

CTR_01

CTR_02

CTR_03

CTR_04

CTR_05
16

Fig. 22 Synchronized lower-tibia load histories

in the ATD lower-leg loading 

Fig. 23 Relation between the ATD lower-tibia load

and CTR crosshead acceleration in each loading condition

There are 2 regions in the amplitude–domain transfer relation: nonlinear and linear (Fig. 24). 

Moreover, there is a rate effect in the slopes of the nonlinear region, whereas the slopes in the 

linear region are almost the same among test conditions and smaller than those of the nonlinear 

region. The smaller slopes in the linear regions are probably due to the plateau regions in the 

ATD lower-leg responses (shown in Fig. 22). The boundary between the nonlinear region and 

linear region was defined as the inflection point of the bilinear curve in the nonlinear region.

0

2

4

6

8

10

-10 -5 0 5 10

Load (kN)

Time(msec)

ATD_01

ATD_02

ATD_03

ATD_04

ATD_05

-1

0

1

2

3

4

5

6

7

8

9

10

-2,500 0 2,500 5,000 7,500

Load (kN)

Acceleration (m/s2)

CTR_01 / ATD_01

CTR_02 / ATD_02

CTR_03 / ATD_03

CTR_04 / ATD_04

CTR_05 / ATD_05
17

Fig. 24 Schematic of the amplitude–domain transfer relation between

the CTR response and ATD lower-leg response

Considering the above, the amplitude–domain transfer relation was formularized. In the

nonlinear region, the ATD lower-tibia load FLEG is calculated as follows:

FFAAAAAA = AA ∙ aaCC CC

2 + BB ∙ aaCC CC , (1)

where aCTR is the acceleration of the CTR crosshead, and A and B are the rate-dependent 

parameters in a loading condition. In the linear region, FLEG is calculated as follows:

FFAAAAAA = CC ∙ aaCC CC + FFIIII , (2)

where FIP is equal to FLEG calculated in Eq.1 at the inflection point of the bilinear curve, and C is 

the averaged slope in the linear region among loading conditions. The Parameters A, B, and C 

were calculated for each loading condition (Table 6). Moreover, in the application of this transfer 

relation to other loading conditions, the parameters were calculated as the bilinear interpolation 

of the values in Table 6 according to the velocity change ∆V. 

Table 6 Parameters for Eqs. 1 and 2 in each loading condition Load (ATD LL)

0

∆V=Low

∆V=High

∆V=Mid

Linear

Region

Non-Linear

Region

Acceleration (CTR)

Units: Load(kN), Acceleration(m/s2), Time(msec)

7.29E-03

6.96E-03

CTR_05 / ATD_05 6.62 -3.97E-06 1.10E-02

CTR_01 / ATD_01

CTR_03 / ATD_03

3.52

5.26

-5.61E-06

-2.22E-06 3.20E-04

Loading

Condition

Velocity

Change,

∆V(m/s)

A B C
18

Similar procedures were applied in the duration–domain comparison. Firstly, the responses of the 

CTR and ATD lower leg were normalized by their peak values. Secondly, as shown in Figs. 25 

and 26, the relation between the duration and normalized response were analyzed according to 

the SAE J1727 injury-calculations guideline for decomposing the time domain signal into the 

duration domain signal. 

Fig. 25 Relation between the duration and normalized

response of the CTR loading

Fig. 26 Relation between the duration and normalized

response in the ATD lower-leg loading 

The responses of both test configurations were related in the duration domain as shown in

Fig. 27. In this study, we focused on the 5-msec-pulse loading. Therefore, the maximum pulse 

duration is at most 8 msec in the CTR response, and we focus on the linear part of the duration–
19

domain transfer relation (Fig. 28). Thus, the ATD lower-tibia time duration TATD is calculated as 

follows:

TTAAAAAA = DD ∙ TTCC CC , (3) 

where TCTR is the CTR time duration. The parameter D was calculated as listed in Table 7 for 

each loading condition. In the application of this transfer relation to other loading conditions, the 

parameter was calculated as the linear interpolation of the value in Table 7 according to the ∆V. 

The ATD lower-leg response is predicted from the CTR response combining the amplitude–

domain transfer and duration–domain transfer; a CFC600 filter is applied to ensure consistency 

with the appropriate lower-leg filter class from the CTR response.

10

Fig. 27 Relation of the pulse duration between the

ATD lower-tibia response and CTR crosshead

response in each loading condition

0

5

10

15

20

0 5 10 15 20

ATD Lower Leg Duration (msec)

CTR Duration (msec)

CTR_01 / ATD_01

CTR_02 / ATD_02

CTR_03 / ATD_03

CTR_04 / ATD_04

CTR_05 / ATD_05
20

Fig. 28 Schematic of the duration–domain transfer relation between

the CTR response and ATD lower-leg response

Table 7 Parameters for Eq. 3 in each loading condition 

3.2 Prediction of ATD Lower-Leg Response Based on the CTR Response

To confirm the validity, the transfer relation was applied to the CTR responses of 2 SKYDEX 

tests, which were not used in the development of the transfer relation. The predicted ATD 

responses are shown in Figs. 29 and 30 with the experimental ATD responses. To confirm the 

validity against other floor-mat material, the transfer relation was applied to the butyl-rubber 

floor mat using the FE model of the CTR and ATD lower leg. The FE-material model used for 

the butyl rubber in these FE models is listed in Table 8.9 Duration (ATD LL)

0 Duration (CTR)

∆V=Low

∆V=High

∆V=Mid

Linear

Region

Loading

Condition

Velocity

Change,

∆V(m/s)

D

CTR_01 / ATD_01 3.52 1.84

Units: Load(kN), Acceleration(m/s2), Time(msec)

CTR_03 / ATD_03 5.26 1.41

CTR_05 / ATD_05 6.62 1.10
21

Fig. 29 Comparison between the ATD lower-leg

experimental response and predictive response

from the CTR response, CTR_02/ATD_02 (∆V = 4.86 m/s) 

Fig. 30 Comparison between the ATD lower-leg

experimental response and predictive response

from the CTR response, CTR_04/ATD_04 

(∆V = 6.26 m/s) 

0

2,000

4,000

6,000

8,000

10,000

12,000

0

2

4

6

8

10

12

-20 -15 -10 -5 0 5 10 15 20

Acceleration (m/s2)

Load (kN)

Time (msec)

ATD LL Load (Experiment)

ATD LL Load (Prediction)

CTR Acceleration

0

2,000

4,000

6,000

8,000

10,000

12,000

0

2

4

6

8

10

12

-20 -15 -10 -5 0 5 10 15 20

Acceleration (m/s2)

Load (kN)

Time (msec)

ATD LL Load (Experiment)

ATD LL Load (Prediction)

CTR Acceleration
22

Table 8 FE-material models for the butyl rubber

The predicted ATD response from the CTR response in the FEA is shown in Fig. 31 with the 

ATD response in the FEA. The prediction errors of these comparisons are listed in Table 9. 

The predicted ATD responses agree with those of the experiments including the plateau regions 

(second peaks), whereas the clues are not clear in the CTR responses. Especially, the peak loads 

are well predicted. However, the prediction overestimates the ATD lower-leg response in the 

large ∆V loading. The treatment of the high acceleration in the CTR response needs to be 

revisited to increase the accuracy of the transfer relation.

In the application to the butyl-rubber floor mat, the prediction in the amplitude domain shows 

small errors. However, the prediction in the duration domain shows shorter duration response 

than the FEA result of the ATD lower leg. Thus, the impulses are underestimated. This may be 

because of the low reliability of the FE-material model in the unloading phase. Therefore, the 

experimental confirmation against other available material is anticipated.

Fig. 31 Example of the application of the transfer relation 

to the butyl-rubber floor mat in the FEA, 

CTR_03/ATD_03 (∆V = 5.26 m/s) 

0

2,000

4,000

6,000

8,000

10,000

12,000

0

2

4

6

8

10

12

-20 -15 -10 -5 0 5 10 15 20

Acceleration (m/s2)

Load (kN)

Time (msec)

ATD LL Load

(ATD LL FEA)

ATD LL Load

(Prediction from CTR FEA)

CTR Acceleration
23

Table 9 Errors in the ATD lower-leg response prediction from the CTR response

4. Conclusions 

In this study we developed the CTR to replace the ATD lower leg in the evaluation of the floor 

mat against underbody blast loading. Through the FEA, the CTR was designed to simulate the 

floor-mat loading status under the ATD lower leg during the loading event. Then, the transfer 

relation between the CTR response and ATD lower-leg response was clarified through the drop 

test with various loading conditions. Moreover, the validity and applicability of the transfer 

relation were confirmed with the experimental results of SKYDEX loading and FEA results of 

the butyl-rubber loading.

Through these processes, the CTR prototype was developed with the transfer relation for the 

prediction of ATD lower-leg response. For the improvement of the CTR, further loading tests 

with large ∆V and other floor mats are recommended. 

4.86

Prediction

Error in the

Peak Load

Prediction

Error in the

Applied Impulse

-8% 37%

Floor mat

material

Loading

Condition

Butyl Rubber

SKYDEX

SKYDEX CTR_02 / ATD_02

CTR_04 / ATD_04

CTR_05 / ATD_05

6.26

5.26

18%

2%

-4%

-24%

Velocity

Change,

∆V(m/s)
24

5. References 

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. Kargus RG. Laboratory evaluation of blast mitigating floor mats. Adelphi (MD): Army 

Research Laboratory (US); 2013 Jan. Report No.: (Sensitive Information Redacted Version). 

8. Bailey AM, Panzer MB, Salzar RS. Development of a Hybrid-III to human leg transfer 

function for axial loading. Paper presented at: 10th Annual Injury Biomechanics Symposium. 

Proceedings of the Ohio State University Injury Biomechanics Symposium; 2014 May 18–

20; Columbus (OH).

9. Sakamoto M. Experimental validation of the butyl-rubber finite element (FE) material model 

for the blast-mitigating floor mat. Adelphi (MD); Army Research Laboratory (US). 2015 

Aug. Report No.: ARL-SR-0329.

10. Memorandum for Record. Updated accelerative loading criteria for crew injury. Army 

Research Laboratory (US); 2012 May. 
25

List of Symbols, Abbreviations, and Acronyms

ARL US Army Research Laboratory

ATD anthropomorphic test device

CSBES Crew Survivability Blast Effects Simulator

CTR Compression Test Rig

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 
26

 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