The Effects of Layer Constraint on Stress Wave Propagation 

in Multilayer Composite Materials 

by Alper Tasdemirci, Ian W. Hall, Bazle A. Gama, and Mustafa Guden 

ARL-CR-550 September 2004 

prepared by 

Department of Mechanical Engineering 

University of Delaware 

Center for Composite Materials 

Newark, DE 19716 

under contract 

DAAD19-01-2-0001 

Approved for public release; distribution is unlimited. 
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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5069 

ARL-CR-550 September 2004 

The Effects of Layer Constraint on Stress Wave Propagation 

in Multilayer Composite Materials 

Alper Tasdemirci, Ian W. Hall, and Bazle A. Gama 

Department of Mechanical Engineering and 

Center for Composite Materials 

University of Delaware 

Mustafa Guden

Department of Mechanical Engineering, 

Izmir Institute of Technology 

prepared by 

Department of Mechanical Engineering 

University of Delaware 

Center for Composite Materials 

Newark, DE 19716 

under contract 

DAAD19-01-2-0001 

Approved for public release; distribution is unlimited. 
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The Effects of Layer Constraint on Stress Wave Propagation in Multilayer 

Composite Materials 

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6. AUTHOR(S) 

Alper Tasdemirci,* Ian W. Hall,* Bazle A. Gama,* and Mustafa Guden†

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University of Delaware 

Department of Mechanical Engineering 

Center for Composite Materials 

Newark, DE 19716 

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*Department of Mechanical Engineering and Center for Composite Materials, University of Delaware, Newark, DE 19716 

†

Department of Mechanical Engineering, Izmir Institute of Technology, Izmir, Gulbahce, Turkey 

14. ABSTRACT 

Multilayer materials consisting of ceramic and glass/epoxy with a rubber interlayer have been subjected to a high strain rate 

compression using a split-Hopkinson Pressure Bar (SHPB). The feasibility of modeling stress wave propagation in complex 

multilayer materials has been demonstrated. It has been shown that the effects of lateral confinement of a normally 

low-modulus interlayer material can significantly affect the response to wave propagation. 

Numerical modeling clearly shows that severe stress inhomogeneities and discontinuities exist, and these may have serious 

consequences for the mechanical and other properties. The one-dimensional stress state usually assumed for conventional 

SHPB testing is therefore inapplicable, and both numerical and experimental results have to be coupled for a complete 

understanding of the wave propagation characteristics. In this study, both methods were used, and the stress states inside the

components were presented. 

15. SUBJECT TERMS

multilayer structures, finite element analysis, mechanical properties, high strain rate 

16. SECURITY CLASSIFICATION OF: 

19a. NAME OF RESPONSIBLE PERSON

Alper Tasdemirci 

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UNCLASSIFIED 

b. ABSTRACT 

UNCLASSIFIED

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OF ABSTRACT 

UL 

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OF PAGES 

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Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18
iii

Contents 

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

2. Experiments and Modeling 2

3. Results 5

3.1 Impact Velocity (10 m/s).................................................................................................5 

3.2 Impact Velocity (16 m/s).................................................................................................6 

3.3 Impact Velocity (20.5 m/s)..............................................................................................9 

4. Discussion 13

5. Conclusions 17

6. References 18

Distribution List 21 
iv

List of Figures 

Figure 1. (a) Constrained sample prior to testing and (b) schematic of setup. ...............................3 

Figure 2. Stress on the incident and transmitter bars during a test at 10 m/s 

(unconstrained-rubber): (a) experimental and (b) calculated....................................................6 

Figure 3. (a) Experimental and (b) calculated stress on ceramic: (c) experimental and 

(d) calculated stress on composite (unconstrained-rubber, V = 10 m/s)....................................7 

Figure 4. Stress on the incident and transmitter bars during a test at 10 m/s 

(constrained-rubber): (a) experimental and (b) calculated.......................................................8 

Figure 5. Stress on the specimen (constrained-rubber) tested at 10 m/s: (a) experimental and 

(b) calculated stress on ceramic: (c) experimental and (d) calculated stress on composite......9 

Figure 6. Stress measured on the incident and transmitter bars during a test at 16 m/s: 

(a) unconstrained rubber and (b) constrained rubber...............................................................10 

Figure 7. Experimental data from ceramic/rubber/composite tested at 16 m/s. Stress 

measured on (a) ceramic and (b) composite. ...........................................................................10 

Figure 8. Calculated output from strain gages on the incident and transmitter bars during a 

test at 16 m/s: (a) unconstrained rubber and (b) constrained rubber.......................................11 

Figure 9. Calculated data from ceramic/rubber/composite (V = 16 m/s). Stress measured on 

(a) ceramic and (b) composite..................................................................................................11 

Figure 10. Stress on the incident and transmitter bars during a test at 20.5 m/s on an 

unconstrained ceramic/rubber/composite: (a) experimental and (b) calculated. ....................12 

Figure 11. Stress measured on ceramic: (a) experimental and (b) calculated. Stress 

measured on composite: (c) experimental and (d) calculated (unconstrained-rubber, 

V = 20.5 m/s). ..........................................................................................................................13 

Figure 12. Stress measured on the incident and transmitter bars during a test at 20.5 m/s on a 

constrained ceramic/rubber/composite: (a) experimental and (b) calculated. ........................14 

Figure 13. Stress measured on ceramic: (a) experimental and (b) calculated: Stress 

measured on composite: (c) experimental and (d) calculated (constrained-rubber, 

V = 20.5 m/s). ..........................................................................................................................15 

List of Tables 

Table 1. Material properties used in finite element models............................................................5 
v

Acknowledgments 

The authors gratefully acknowledge financial support for this research under the Composite 

Materials Research Collaborative Program sponsored by the U.S. Army Research Laboratory, 

contract number DAAD19-01-2-0001. 
vi

INTENTIONALLY LEFT BLANK. 
1

1. Introduction 

Thick-section composite materials are frequently used under dynamic loading conditions, but 

their behavior is still not clearly understood. Impact loading of monolithic laminates has been 

the subject of several investigations, e.g., with glass/epoxy and graphite/epoxy (1–10). Similarly 

the penetration or perforation of composites has also been studied (11, 12), but severe 

complications arose whenever widely dissimilar materials well in intimate contact because their 

differing impedances caused complex wave reflection and transmission phenomena at each 

interface encountered. Thick, layered, or graded structures have significant potential for armor 

applications, and Li et al. (13) reported the dynamic characterization of layered and graded 

structures under impulsive loading. Another example of multilayer materials is provided by 

modern integral composite armor for vehicle applications as described by Fink (14) and 

Gama et al. (15–17). The armor material must provide ballistic protection at minimum weight 

and may contain several layers of different impedance, usually a ceramic layer followed by a 

thick composite plate (e.g., glass fiber/epoxy). High-velocity impact of this type of integral 

armor has been the subject of finite element studies by Mahfuz et al. (18). Jovicic et al. (19) 

modeled the ballistic behavior of gradient design composite armors. 

The elastic adhesives used in composite armors can also alter wave propagation in the armor 

components. The mechanical behavior of different elastic adhesives under impact loads was 

studied by Martinez et al. (20) who reported that the capability of transmitting and reflecting the 

impact energy depends on the thickness and the type of the adhesive used. They concluded that 

the utilization of a thin layer of a rigid adhesive was the best way to transmit energy with the 

lowest reflection coefficient. 

A central concept in enhancing the ability of multilayer material structures to withstand rapid 

impulsive loading is to spread the local impact load as rapidly and widely as possible. This can 

be achieved by placing a high wave-speed layer in the layered system. Gupta and Ding (21) 

studied numerically the effects of wave speed, layering geometry, and mechanical properties of 

the layer and substrate on load spreading. They showed that for a fixed layer thickness, a single 

thick high-strength high wave-speed layer appears to be able to offer the best lateral load 

spreading through intense and rapid wave transmission and spreading. The low wave-speed 

material used in multilayered targets appears to deteriorate the load spreading capability of the 

layered system. 

Design of efficient multilayer materials for impact resistance requires both modeling and 

experimental efforts, and the split-Hopkinson pressure bar (SHPB) is a convenient tool in the 

latter respect although conventional data reduction routines obviously cannot be used for these 

materials. Two- and three-dimensional (2-D and 3-D) wave propagation in Hopkinson bar tests 
2

has been investigated numerically by several authors (22, 23). In experimental studies, impact 

velocity of the striker bar and axial strain on the bar surfaces are the most commonly measured 

quantities. In numerical studies, besides the parameters previously mentioned, displacement and 

velocity of nodes, strain and stress of the elements, and interface forces can all be acquired as a 

function of time (24). 

Prior work (25) addressed the situation with three different layers consisting of ceramic, rubber 

and composite, in which lateral expansion of the rubber was permitted. However, in practical 

large-scale structures, the rubber interlayer would be constrained by the surrounding material, 

and this present report considers the effects of such lateral constraint on the resulting properties. 

Samples used in SHPB testing can, at the most, have the same diameter as the bar, and earlier 

experiments showed that considerable radial flow occurred in the rubber interlayer. Larger 

samples, typical of many anticipated applications, would be subjected to severe lateral 

constraints which would, in turn, affect the through-thickness stresses reported. In fact, the real 

case will probably lie somewhere between the extremes of completely constrained and 

completely unconstrained interlayers, so the evaluation of both limiting cases is correspondingly 

important. 

The effect of lateral constraint on ballistic performance has been investigated by many authors, 

and it is now well known that a compressive prestress is helpful in improving the fracture energy 

and impact resistance in brittle materials. Espinosa et al. (26) experimentally studied the impact 

resistance of ceramics confined in steel fixtures and showed the enhancement of ballistic 

efficiency of the confined ceramics. Martinez et al. (20) have determined the stress-strain curve 

of confined adhesive used in armor at high strain rates. Within the armor, elastic adhesives, 

comparable with the rubber interlayer in our case, were used to bond two large plates of much 

more rigid materials, which themselves impede subsequent lateral displacements of the adhesive. 

This study, then, presents the initial results of a combined experimental and numerical 

investigation and serves to delineate the principal features and identify the problems to be solved 

in order to develop a better understanding of the effects of constraint in such multilayer 

materials. 

2. Experiments and Modeling 

Samples were prepared from multilayer plates with layers of widely different impedances. The 

plates consisted of three layers, namely a 13.96-mm-thick alumina ceramic, a 1.5-mm-thick layer 

of ethylene propylene diene monomer (EPDM) rubber, and a layer of glass/epoxy composite. 
3

The 5 × 5 plain weave S-2 Glass* fiber woven fabric (0.814 kg/m2) SC15† epoxy (toughened 

resin) composite plates were 11.3-mm-thick and were produced using the vacuum-assisted resin 

transfer molding process. Lateral confinement of the rubber interlayer was obtained by placing a 

6-mm-wide steel retaining ring around the junction of the sample as illustrated in figure 1. An 

interference fit was achieved between the rubber and the steel ring, and no rubber was squeezed 

out into the region between them while testing. Possible inertial effects and interactions between 

the ring and the other components of the sample were checked via tests on individual ceramic 

and composite samples with the ring in place. No modification to the wave propagation behavior 

was observed in the presence of the steel ring. The ceramic layer was always at the impacted 

side. 

 

(a) (b)

Figure 1. (a) Constrained sample prior to testing and 

(b) schematic of setup. 

Cylindrical samples, 15.7 mm in diameter, were core drilled from the plates in the 

through-thickness direction. Samples were compression tested over a wide range of 

displacement rates using the SHPB apparatus (the compression axis normal to fiber plane). 

However, the focus of the present report concerns a series of tests, all of which were conducted 

with striker bar velocities of 10, 16, or 20.5 m/s—as an approximate guide, these velocities 

would generate “average strain rates” of ~400, 500, and 700/s, respectively. 

The particular SHPB apparatus used consists of Inconel‡ 718 bars, a 356-mm-long striker bar, 

3450-mm incident, and 1850-mm transmitter bars, all with a diameter of 19 mm. Further details 

of the experimental setup and standard data reduction routines are available elsewhere (27). 

Samples were fitted with strain gages, as shown in figure 1, so as to monitor real-time 

strains/stresses during the course of the tests. Strain gages with 0.79-mm element lengths were

 *

S-2 Glass is a registered trademark of Owens Corning. 

†

SC15 is a trademark of Applied Poleramic Incorporation.. 

‡

Inconel is a registered trademark of the INCO family of companies. 
4

used generally, although several tests were also carried out with an array of gages designed to 

sample the strain simultaneously at several locations along the sample length and thus provide a 

strain/time/position map of the wave passage. 

A 3-D SHPB finite element model was used to study stress wave propagation in the multilayer 

materials and also in the individual components. Rubber is a highly nonlinear elastic material 

and the role of this nonlinear material has been studied by modeling the rubber layer with 

experimentally determined material data. The analyses were performed using a commercial 

explicit finite element code LS-DYNA 960. Two axes of symmetry were assumed, so only one 

quarter of the bar was modeled. For each test modeled, the output was displayed at several 

locations, within the sample as well as at the location of the strain gages on the incident and 

transmitter bars of the SHPB apparatus. The desired ideal result is that output from the strain 

gages on the incident and transmitter bars closely match data calculated from the model. 

Similarly, output measured by gages on the sample should also closely match data calculated 

from the model. When both these conditions are met, it indicates that the model is accurately 

capturing the wave propagation behavior in the sample and bars. 

The model has four components in contact: a striker bar of 356 mm in length, an incident bar 

and a transmission bar each of 1524 mm in length, and the specimen, i.e., the ceramic, rubber, 

and composite layers, the thicknesses of which are 14, 1.5, and 10.6 mm, respectively. The bar 

diameter is 19.05 mm, and the diameter of the specimen is 16.0 mm. The component materials 

are modeled with 8-node solid elements, and the interfaces are modeled with the automatic 

contact sliding interfaces without friction. The impact velocity of the striker bar (V = 10, 16, and 

20.5 m/s) has been defined as the initial condition, and all other boundaries are traction free and 

can move in any direction. In order to save computation time, the simulation uses bars 1524 mm 

in length, instead of full length bars. It will be seen later from the figures that this has the effect 

of decreasing the transit time between successive waves and shortening the wave duration 

slightly, however, it does not affect the basic wave shapes or amplitudes. A few trial 

computations were carried out using full-length bars, but apart from the slightly smaller time 

window, no significant differences were found, and the shorter bars were used henceforth. 

Material properties used in the finite element code are shown in table 1. The ceramic was 

modeled with an isotropic elastic material model, and the composite was modeled with an 

orthotropic elastic material. Rubber was modeled with two different material models. The 

Mooney-Rivlin Model (28) (two parameter nonlinear material model) was used for the 

unconstrained configuration and the Blatz-Ko Material Model (28) was used for the constrained 

configuration. The Blatz-Ko Material Model shows better agreement for the hydrostatic state of 

stress of the rubber. For the unconstrained case, the rubber interlayer deforms very extensively, 

and this large deformation caused stability problems in the finite element model. This problem 

was solved by using different material parameters for the different cases. While higher shear 

modulus values give better results for the constrained case, in unconstrained samples, the lower 

shear modulus values give better agreement with the experimental results. Actual compression 
5

tests on the rubber itself confirm that this behavior is indeed observed in practice. To be able to 

use the same material model would probably be preferable, and this will be implemented for 

future simulations. The Inconel bars were modeled with an isotropic elastic material model, and 

lateral confinement of the rubber interlayer was modeled by preventing the displacements in both 

x and y directions for this component. 

Table 1. Material properties used in finite element models. 

Material 

Modulus of 

Elasticity 

(GPa) 

Poisson’s Ratio Density 

(kg/m3

) 

Other 

Ceramic 370 0.22 3900 — 

Mooney-Rivlin 

rubber 

— 0.495 1200 A:0.2 (MPa) 

B: 0.8 (MPa) 

Blatz-Ko rubber — 0.493 1200 G: 20 (MPa) 

Composite 

E1: 40 

E2: 40 

E3: 15 

ν21: 0.12 

ν31: 0.173 

ν32: 0.173 

1668 

G1: 8 (GPa) 

G2: 8 (GPa) 

G3: 8 (GPa) 

Inconel 207 0.3 7850 — 

3. Results 

The experimental results are presented here in order of increasing incident bar velocity which 

corresponds to increasing loading rate and, as will become clear, increasing degrees of damage 

within the samples. Three different striker bar velocities were used, and SHPB tests and 

simulations were performed for both the unconstrained and the constrained situations. The 

primary data for each test consist of (1) experimental output from the SHPB bars for constrained 

and unconstrained specimens, (2) measured strain gage data from each sample, and (3) numerical 

data, which are then compared with the corresponding experiments. 

3.1 Impact Velocity (10 m/s) 

Figure 2 shows experimental and calculated SHPB data from an unconstrained sample tested at a 

striker bar velocity of 10 m/s, and close agreement is noted between the experimental and 

numerical results. Experimentally, it is seen that the transmitted wave amplitude slowly 

increases to ~60 MPa as indicated and exhibits a minor peak of ~100 μs before that. Calculated 

data show almost identical behavior. 

Experimental data from the ceramic portion of an unconstrained strain-gaged sample are shown 

in figure 3a, while figure 3b shows the corresponding numerical data. The insets in the figure 

indicate the location of the gages or nodes interrogated. First, it is noted that the stress varies 

greatly with time and, second, it is noted that the stress close to the incident bar/ceramic interface 
6

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0 100 200 300 400 500 600 700

Stress, MPa.

time, micro-seconds.

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0 100 200 300 400 500 600 700

Stress, MPa.

time, micro-seconds.

(a) (b) 

Figure 2. Stress on the incident and transmitter bars during a test at 10 m/s (unconstrained-rubber): (a) 

experimental and (b) calculated. 

is invariably greater than that closer to the ceramic/rubber interface. Similarly, figure 3c and d 

shows experimental and calculated stresses measured on the composite portion of the sample. 

Note that the magnitude of the initial peak in the composite layer is less than that in the ceramic 

layer and, again, an inhomogeneous stress distribution exists. Also, fewer large stress 

oscillations are noted than in the case of the ceramic. Generally, the numerical data show 

broadly similar behavior to the experimental data in each case, including multiple peaks in the 

ceramic, similar scale of stress inhomogeneity, similar magnitudes of the maximum stress, and a 

similar overall shape to each stress vs. time curve. 

Figure 4 shows experimental and numerical SHPB data from a sample, tested at a striker bar 

velocity of 10 m/s, in which the rubber interlayer was constrained. Comparison with 

corresponding unconstrained data (figure 2a and b) shows that constraint greatly modifies the 

reflected and transmitted wave shapes. The constrained sample exhibits a maximum transmitted 

wave amplitude of ~200 MPa as compared to ~60 MPa for the unconstrained case. Figure 5 

shows experimental and calculated stresses within the ceramic and composite, as a function of 

time, at different locations within the sample. It shows significantly different behavior compared 

to the unconstrained data, namely, what is essentially a single peak in the ceramic and composite 

and a more rapidly rising stress in both of the components when the rubber interlayer is 

constrained. The peak stress values in each component are almost the same value, i.e., 

~250 MPa—considerably higher than when the rubber is unconstrained. 

3.2 Impact Velocity (16 m/s) 

When tested at an intermediate velocity, samples began to suffer limited damage, although none 

failed catastrophically. Lateral constraint of the rubber interlayer was found to increase the 

time, microseconds time, microseconds 
7

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A C

Stress, MPa.

time, microseconds.

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A C

Stress, MPa.

time, microseconds. 

 (a) (b) 

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D F

Stress, MPa.

time, microseconds.

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250 300 350 400 450 500 550 600

D F

Stress, MPa.

time, microseconds.

(c) (d) 

Figure 3. (a) Experimental and (b) calculated stress on ceramic: (c) experimental and (d) calculated stress on 

composite (unconstrained-rubber, V = 10 m/s). 

damage level in both of the components. Visual damage in the composite exhibited itself as 

lateral spreading of the layers accompanied by significant radial strain, whereas the ceramic only 

exhibited occasional and limited spalling from the edges of the impacted face. 

Figure 6a and b shows experimental SHPB data for the trilayer ceramic/rubber/composite with 

the rubber layer unconstrained and constrained, respectively. It is clear that the shapes of the 

transmitted and reflected waves for the constrained configuration are drastically different from 

the unconstrained case.
8

 

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0 100 200 300 400 500 600 700

Stress, MPa.

time, micro-seconds.

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0 100 200 300 400 500 600 700

Stress, MPa.

time, micro-seconds.

 (a) (b) 

Figure 4. Stress on the incident and transmitter bars during a test at 10 m/s (constrained-rubber): 

(a) experimental and (b) calculated. 

Major differences in the wave propagation characteristics, caused by lateral confinement of the 

rubber interlayer, are also clearly demonstrated in strain gage data collected from the separate 

layers. Figure 7a and b shows experimental data from the ceramic and composite layers, 

respectively. Data from gages on the ceramic show a marked increase in the measured stress 

levels resulting from confinement (figure 7a). Nevertheless, the general complexity of the wave 

forms of the unconstrained sample remains reminiscent of those tested at lower velocity (see 

figure 3a) insofar as three peaks may be discerned at ~65-μs intervals. The peaks present in the 

unconstrained case merge into essentially one peak when the rubber is constrained. In the 

composite, the maximum stress level experienced with constraint of the rubber interlayer is 

~2.5× that for the unconstrained sample (figure 7b), while the corresponding stress in the 

ceramic increases by a factor of ~3.3. 

Figure 8a and b shows the calculated data from the Hopkinson bars. For these samples, 

agreement between the experimental (figure 6a and b) and numerical data is currently slightly 

less close than for the low-velocity case, principally because damage has begun to occur in the 

experimental samples, but damage mechanisms have not yet been included in the present model, 

although they have been discussed elsewhere (29). The effect of damage initiation is reflected in 

a truncation of the early peak in the measured reflected wave. 

Figure 9a and b shows numerical data from the individual ceramic and composite layers for the 

constrained and unconstrained cases. The elements chosen for the numerical data were at 

approximately the same position as the strain gages reported in figure 7. Comparison of these 

two figures shows that the calculated stress magnitudes are very similar to the experimental 

time, microseconds time, microseconds 
9

 

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0

250 300 350 400 450 500 550 600

B

Stress, MPa.

time, microseconds.

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B

Stress, MPa.

time, microseconds.

 (a) (b) 

 

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E

Stress, MPa.

time, microseconds.

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E

Stress, MPa.

time, microseconds.

 (c) (d) 

Figure 5. Stress on the specimen (constrained-rubber) tested at 10 m/s: (a) experimental and 

(b) calculated stress on ceramic: (c) experimental and (d) calculated stress on composite. 

values. They differ only very slightly in detail as a result of the slight “stress-averaging” effect 

due to the finite size of the gages and, despite this, the same general shapes are found. 

3.3 Impact Velocity (20.5 m/s) 

A similar set of experiments and simulations was then carried out for a higher striker bar 

velocity. Now the presence of the rubber interlayer and its constraint leads to major differences 

in the wave propagation characteristics. Figure 10a and b shows experimental and calculated 

data from the incident and transmitter bars for the unconstrained rubber case. For this 

configuration, the basic shapes and magnitudes of the transmitted waves resemble each other, but 
10

 

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Stress, MPa.

time, micro-seconds.

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0 100 200 300 400 500 600 700

Stress, MPa.

time, micro-seconds.

 (a) (b) 

Figure 6. Stress measured on the incident and transmitter bars during a test at 16 m/s: (a) unconstrained 

rubber and (b) constrained rubber. 

 

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unconstrained (B)

constrained (B)

Stress, MPa.

time, microseconds.

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0

250 300 350 400 450 500 550 600

unconstrained (E)

constrained (E)

Stress, MPa.

time, microseconds.

 (a) (b) 

Figure 7. Experimental data from ceramic/rubber/composite tested at 16 m/s. Stress measured on (a) ceramic 

and (b) composite. 

it is evident that significant physical damage begins to occur during the test at a stress of 

~400 MPa, most clearly indicated by a change in the reflected wave shape. 

Figure 11 shows experimental and numerical data from the individual ceramic and composite 

layers, respectively, with an unconstrained rubber interlayer. Figure 11a and c shows the actual

time, microseconds time, microseconds 
11

 

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Stress, MPa.

time, micro-seconds.

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Stress, MPa.

time, micro-seconds.

 (a) (b) 

Figure 8. Calculated output from strain gages on the incident and transmitter bars during a test at 16 m/s: 

(a) unconstrained rubber and (b) constrained rubber. 

 

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unconstrained (B)

constrained (B)

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time, microseconds.

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unconstrained (E)

constrained (E)

Stress, MPa.

time, microseconds.

 (a) (b) 

Figure 9. Calculated data from ceramic/rubber/composite (V = 16 m/s). Stress measured on (a) ceramic and 

(b) composite. 

stress measured from two strain gages close to incident bar and rubber interfaces of the sample 

for the ceramic and, similarly, for the composite. (During this particular experiment, the gage 

close to the transmitter bar interface on the composite broke off due to the high strain at this 

location. As a result, only the initial portion of the stress read-out can be recorded for this gage.) 

Figure 11b shows the z-stress in the ceramic layer, calculated at two elements, at almost the same 

time, microseconds time, microseconds 
12

 

-600

-400

-200

0

200

400

600

0 100 200 300 400 500 600 700

Stress, MPa.

time, micro-seconds.

-600

-400

-200

0

200

400

600

0 100 200 300 400 500 600 700

Stress, MPa.

time, micro-seconds.

 (a) (b) 

Figure 10. Stress on the incident and transmitter bars during a test at 20.5 m/s on an unconstrained 

ceramic/rubber/composite: (a) experimental and (b) calculated. 

location as the experimental case. It can be clearly seen that during the course of testing the 

material experiences a nonuniform stress distribution, with the minimum occurring close to the 

rubber interlayer. Figure 11d shows calculated data from a similar element on the composite 

layer. Despite possible limitations of the present model due to damage initiation, it is seen that 

the calculated maximum stress levels are still very close to the measured stresses. 

Figure 12a and b shows measured and calculated data from the incident and transmitter bars for 

the constrained rubber case. For these samples, agreement between the experimental and 

numerical data is again less close than for the unconstrained case at lower striker bar velocities 

(figures 6b and 8b) and the peak value of the reflected pulse has again been somewhat 

overestimated. 

Figure 13 presents experimental and numerical data from the individual ceramic and composite 

layers. Figure 13a and c shows the actual stress measured from a single strain gage at midlength 

of the sample for the ceramic and composite. Similarly, figure 13b and d shows numerical data 

from the individual ceramic and composite layers at comparable locations. Comparison with 

figure 11 shows that a major effect of constraint is to broaden the principal peaks, resulting in the 

components remaining longer at these higher stress levels. The maximum stress is still 

experienced in each case (~140 μs) after the initial impact. Even for this high-impact velocity, 

the model still captures the general features of wave propagation and the form of stress 

distribution. The agreement in terms of absolute values of stress can also be clearly seen from 

the figures. 

time, microseconds time, microseconds 
13

-600

-500

-400

-300

-200

-100

0

250 300 350 400 450 500 550 600

A C

Stress, MPa.

time, microseconds.

-600

-500

-400

-300

-200

-100

0

250 300 350 400 450 500 550 600

A C

Stress, MPa.

time, microseconds.

(a) (b) 

-400

-350

-300

-250

-200

-150

-100

-50

0

250 300 350 400 450 500 550 600

D F

Stress, MPa.

time, microseconds.

-400

-350

-300

-250

-200

-150

-100

-50

0

250 300 350 400 450 500 550 600

D

Stress, MPa.

time, microseconds.

 (c) (d) 

Figure 11. Stress measured on ceramic: (a) experimental and (b) calculated. Stress measured on 

composite: (c) experimental and (d) calculated (unconstrained-rubber, V = 20.5 m/s). 

4. Discussion 

The main objective of the present work was to investigate experimentally and numerically the 

effects of lateral confinement of the rubber interlayer on the wave propagation characteristics of 

the multilayer material over a range of impact velocities. The SHPB is a convenient tool for 

high strain rate testing of homogeneous elastic/plastic materials, but direct interpretation of 

SHPB data is not possible for materials which are nonlinear or of very low or very high 
14

-600

-400

-200

0

200

400

600

0 100 200 300 400 500 600 700

Stress, MPa.

time, micro-seconds.

-600

-400

-200

0

200

400

600

0 100 200 300 400 500 600 700

Stress, MPa.

time, micro-seconds.

 (a) (b) 

Figure 12. Stress measured on the incident and transmitter bars during a test at 20.5 m/s on a 

constrained ceramic/rubber/composite: (a) experimental and (b) calculated. 

impedance relative to the bars, or anisotropic, or composed of several layers of distinctly 

different materials as in the case studied here. However, if numerical simulation procedures can 

be developed which satisfactorily reproduce the output data of SHPB tests, then (a) the tests 

themselves can be better interpreted and (b) simulations can be carried out with increased 

confidence. 

A previous study (25) showed that there was excellent agreement between numerical data and 

actual data measured from the incident and transmitter bars for a two-layer ceramic/composite 

test. That model satisfactorily captured the details of wave transmission. The present three-layer 

model also satisfactorily captures the details of wave transmission, the general features of wave 

propagation, stress magnitudes, and the form of stress distribution, and consequently offers 

considerably enhanced insight into the processes leading to damage generation in such multilayer 

materials. 

The experiments are subject to some limitation because the strain gages average the data over 

their active gage length, which is typically 0.79 mm as compared with ~0.4 mm for the element 

size in the model. Also, the measured stress is seen to be very strongly dependent upon the exact 

placement of the gage within the specimen length. Finally, some of the strain gages mounted on 

the components could not record all the stress wave history either because of their failure or 

because of the high strain levels generated in the components (see figure 11c). 

Keeping these limitations in mind, it can be appreciated that there is nonetheless good agreement 

between experimental and numerical data even for the highest impact velocity tests. For 

example, figure 3a shows experimental data from two gages (5 mm apart) on the ceramic sample 

time, microseconds time, microseconds 
15

-700

-600

-500

-400

-300

-200

-100

0

250 300 350 400 450 500 550 600

B

Stress, MPa.

time, microseconds.

-700

-600

-500

-400

-300

-200

-100

0

250 300 350 400 450 500 550 600

B

Stress, MPa.

time, microseconds.

 (a) (b) 

-500

-400

-300

-200

-100

0

250 300 350 400 450 500 550 600

E

Stress, MPa.

time, microseconds.

-500

-400

-300

-200

-100

0

250 300 350 400 450 500 550 600

E

Stress, MPa.

time, microseconds.

 (c) (d) 

Figure 13. Stress measured on ceramic: (a) experimental and (b) calculated: Stress measured on 

composite: (c) experimental and (d) calculated (constrained-rubber, V = 20.5 m/s). 

surface. After the initial stress peak, a second major peak is observed ~150 μs later; the 

numerical data (figure 3b) likewise show the initial and second peak stresses at approximately 

similar intervals. Furthermore, interpolating to comparable elemental positions, the relative 

magnitudes are quite similar. The absolute magnitudes of the maximum measured stresses are, 

however, slightly different, and this is partially due to reasons of data source location and the 

“averaging” effect of the strain gage size previously mentioned. 

Throughout all the current sets of experiments and simulations, close agreement was achieved 

between the model and experiment. Figures 6a and b and 8a and b show experimental and 
16

calculated data from the Hopkinson bars. Again, the data match closely, showing that 

LS-DYNA accurately captures the details of wave propagation. 

A major conclusion from the present results is that constraint of the rubber layer drastically alters 

the response of the material, and this is most easily demonstrated by the change of the reflected 

and transmitted wave shapes. For example, in the case of the lowest velocity tests, instead of 

reaching a maximum transmitted stress of ~60 MPa, as for the unconstrained case, the maximum 

stress is ~210 MPa when constrained (compare figures 2a and 4a). Also the stress rises 

relatively faster and more uniformly for the second case: basically, lateral confinement of the 

rubber interlayer increases the wave transmission efficiency between the components. 

It can also be seen that the shapes of the wave traveling through the individual ceramic and 

composite layers are widely different in the unconstrained material, an observation that is 

confirmed both by experimental measurements and numerical analysis. For example, figure 3 

shows that an almost instantaneous and rapid stress increase occurs for the ceramic, followed by 

further major oscillations, while the composite shows a largely monotonic and gradual increase 

in stress level. By contrast, in constrained samples, the wave shapes are almost the same for the 

ceramic and composite (see figure 5) and come to resemble the shape of the wave traveling in 

the composite. In other words and in common with many other kinetic processes, the component 

of lowest impedance dominates the process. 

Rubber leads to a highly inhomogeneous stress distribution within the components when it is 

constrained. Generally, the part of the sample close to the unconstrained rubber experiences a 

reduced stress while the remainder may experience a much higher stress level. However, when 

the rubber is constrained, the differences in stress level within the components are greatly 

reduced, although the stress is still by no means homogeneous. 

For the higher velocity tests, agreement between the experimental and numerical data is currently 

slightly less close than for the lower velocity cases (see figures 10–13), for reasons associated 

with damage evolution. During testing at high velocities, the ceramic frequently shattered, and 

various damage modes were activated in the composite. Even though the material models used 

in this study do not include failure parameters, the numerical calculations still capture the general 

features of wave propagation and the form of stress distribution. Obviously, further refinement 

along these lines will significantly improve agreement between experiment and model. 

In this respect, the present work indicates several avenues for characterizing damage evolution in 

these, or similar materials at high strain rates since the effects of damage are clearly indicated in 

the output signals. For example, the principal differences between figures 4a and 10a can be 

ascribed to the onset of significant damage that alters the (here assumed elastic) properties of the 

materials. Therefore, the point at which experimental and numerical data begin to diverge 

probably defines the point at which significant damage begins. It is thus possible to study, by 

comparison of experimental and numerical data, damage evolution at high strain rate indirectly 

as a function of strain and strain rate. When coupled with microscopic examination of recovered 
17

material, the present type of data would elucidate the processes and sequence of deformation and 

fracture events. 

This is potentially of great utility because failure criteria are included in recent material models, 

but a definition of stress and strain levels associated with these events is presently rather 

imprecise. So, if stress or strain levels associated with the onset of various damage mechanisms 

can be determined, these could be inserted into the numerical models and provide improved 

accuracy. 

5. Conclusions 

The present work has demonstrated the feasibility of modeling stress wave propagation in 

complex multilayer materials. It has been shown that the effects of confinement of normally low 

modulus materials can significantly affect their response to wave propagation. Severe stress 

inhomogeneities and discontinuities may exist in multilayer materials, and these may have 

serious consequences for the mechanical and other properties. Numerical modeling clearly 

shows that during Hopkinson bar testing of multilayer materials, stress is not distributed 

uniformly inside the specimen. The one-dimensional stress state usually assumed for 

conventional SHPB testing is questionable, and for a complete understanding of the wave 

propagation, both numerical and experimental results have to be coupled. In this study, both 

methods were used, and the stress states inside the components were presented. Accuracy will 

be increased, especially for the high pressure levels, by implementing damage parameters in 

future material models. 
18

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 CHARLOTTESVILLE VA 

 22911-8318 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

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 1 NAVAL SEA SYSTEMS CMD 

 D LIESE 

 1333 ISAAC HULL AVE SE 1100 

 WASHINGTON DC 20376-1100 

 1 EXPEDITIONARY WARFARE 

 DIV N85 

 F SHOUP 

 2000 NAVY PENTAGON 

 WASHINGTON DC 20350-2000 

 8 US ARMY SBCCOM 

 SOLDIER SYSTEMS CENTER 

 BALLISTICS TEAM 

 J WARD 

 W ZUKAS 

 P CUNNIFF 

 J SONG 

 MARINE CORPS TEAM 

 J MACKIEWICZ 

 BUS AREA ADVOCACY TEAM 

 W HASKELL 

 AMSSB RCP SS 

 W NYKVIST 

 S BEAUDOIN 

 KANSAS ST 

 NATICK MA 01760-5019 

 7 US ARMY RESEARCH OFC 

 A CROWSON 

 H EVERETT 

 J PRATER 

 G ANDERSON 

 D STEPP 

 D KISEROW 

 J CHANG 

 PO BOX 12211 

 RESEARCH TRIANGLE PARK NC 

 27709-2211 

 1 AFRL MLBC 

 2941 P ST RM 136 

 WRIGHT PATTERSON AFB OH 

 45433-7750 

 1 DIRECTOR 

 LOS ALAMOS NATL LAB 

 F L ADDESSIO T 3 MS 5000 

 PO BOX 1633 

 LOS ALAMOS NM 87545 

 8 NSWC 

 J FRANCIS CODE G30 

 D WILSON CODE G32 

 R D COOPER CODE G32 

 J FRAYSSE CODE G33 

 E ROWE CODE G33 

 T DURAN CODE G33 

 L DE SIMONE CODE G33 

 R HUBBARD CODE G33 

 DAHLGREN VA 22448 

 1 NSWC 

 CARDEROCK DIVISION 

 R CRANE CODE 6553 

 9500 MACARTHUR BLVD 

 WEST BETHESDA MD 20817-5700 

 1 AFRL MLSS 

 R THOMSON 

 2179 12TH ST RM 122 

 WRIGHT PATTERSON AFB OH 

 45433-7718 

 2 AFRL 

 F ABRAMS 

 J BROWN 

 BLDG 653 

 2977 P ST STE 6 

 WRIGHT PATTERSON AFB OH 

 45433-7739 

 5 DIRECTOR 

 LLNL 

 R CHRISTENSEN 

 S DETERESA 

 F MAGNESS 

 M FINGER MS 313 

 M MURPHY L 282 

 PO BOX 808 

 LIVERMORE CA 94550 

 1 AFRL MLS OL 

 L COULTER 

 5851 F AVE 

 BLDG 849 RM AD1A 

 HILL AFB UT 84056-5713 

 1 OSD 

 JOINT CCD TEST FORCE 

 OSD JCCD 

 R WILLIAMS 

 3909 HALLS FERRY RD 

 VICKSBURG MS 29180-6199 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

27

 3 DARPA 

 M VANFOSSEN 

 S WAX 

 L CHRISTODOULOU 

 3701 N FAIRFAX DR 

 ARLINGTON VA 22203-1714 

 2 SERDP PROGRAM OFC 

 PM P2 

 C PELLERIN 

 B SMITH 

 901 N STUART ST STE 303 

 ARLINGTON VA 22203 

 1 OAK RIDGE NATL LAB 

 R M DAVIS 

 PO BOX 2008 

 OAK RIDGE TN 37831-6195 

 1 OAK RIDGE NATL LAB 

 C EBERLE MS 8048 

 PO BOX 2008 

 OAK RIDGE TN 37831 

 3 DIRECTOR 

 SANDIA NATL LABS 

 APPLIED MECHS DEPT 

 MS 9042 

 J HANDROCK 

 Y R KAN 

 J LAUFFER 

 PO BOX 969 

 LIVERMORE CA 94551-0969 

 1 OAK RIDGE NATL LAB 

 C D WARREN MS 8039 

 PO BOX 2008 

 OAK RIDGE TN 37831 

 4 NIST 

 M VANLANDINGHAM MS 8621 

 J CHIN MS 8621 

 J MARTIN MS 8621 

 D DUTHINH MS 8611 

 100 BUREAU DR 

 GAITHERSBURG MD 20899 

 1 HYDROGEOLOGIC INC 

 SERDP ESTCP SPT OFC 

 S WALSH 

 1155 HERNDON PKWY STE 900 

 HERNDON VA 20170 

 3 NASA LANGLEY RESEARCH CTR 

 AMSRD ARL VS 

 W ELBER MS 266 

 F BARTLETT JR MS 266 

 G FARLEY MS 266 

 HAMPTON VA 23681-0001 

 1 NASA LANGLEY RESEARCH CTR 

 T GATES MS 188E 

 HAMPTON VA 23661-3400 

 1 FHWA 

 E MUNLEY 

 6300 GEORGETOWN PIKE 

 MCLEAN VA 22101 

 1 USDOT FEDERAL RAILROAD 

 M FATEH RDV 31 

 WASHINGTON DC 20590 

 3 CYTEC FIBERITE 

 R DUNNE 

 D KOHLI 

 R MAYHEW 

 1300 REVOLUTION ST 

 HAVRE DE GRACE MD 21078 

 1 DIRECTOR 

 NGIC 

 IANG TMT 

 2055 BOULDERS RD 

 CHARLOTTESVILLE VA 

 22911-8318 

 1 SIOUX MFG 

 B KRIEL 

 PO BOX 400 

 FT TOTTEN ND 58335 

 2 3TEX CORP 

 A BOGDANOVICH 

 J SINGLETARY 

 109 MACKENAN DR 

 CARY NC 27511 

 1 3M CORP 

 J SKILDUM 

 3M CENTER BLDG 60 IN 01 

 ST PAUL MN 55144-1000 
NO. OF NO. OF 

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 1 DIRECTOR 

 DEFENSE INTLLGNC AGNCY 

 TA 5 

 K CRELLING 

 WASHINGTON DC 20310 

 1 ADVANCED GLASS FIBER YARNS 

 T COLLINS 

 281 SPRING RUN LANE STE A 

 DOWNINGTON PA 19335 

 1 COMPOSITE MATERIALS INC 

 D SHORTT 

 19105 63 AVE NE 

 PO BOX 25 

 ARLINGTON WA 98223 

 1 JPS GLASS 

 L CARTER 

 PO BOX 260 

 SLATER RD 

 SLATER SC 29683 

 1 COMPOSITE MATERIALS INC 

 R HOLLAND 

 11 JEWEL CT 

 ORINDA CA 94563 

 1 COMPOSITE MATERIALS INC 

 C RILEY 

 14530 S ANSON AVE 

 SANTA FE SPRINGS CA 90670 

 2 SIMULA 

 J COLTMAN 

 R HUYETT 

 10016 S 51ST ST 

 PHOENIX AZ 85044 

 2 PROTECTION MATERIALS INC 

 M MILLER 

 F CRILLEY 

 14000 NW 58 CT 

 MIAMI LAKES FL 33014 

 2 FOSTER MILLER 

 M ROYLANCE 

 W ZUKAS 

 195 BEAR HILL RD 

 WALTHAM MA 02354-1196 

 1 ROM DEVELOPMENT CORP 

 R O MEARA 

 136 SWINEBURNE ROW 

 BRICK MARKET PLACE 

 NEWPORT RI 02840 

 2 TEXTRON SYSTEMS 

 T FOLTZ 

 M TREASURE 

 1449 MIDDLESEX ST 

 LOWELL MA 01851 

 1 O GARA HESS & EISENHARDT 

 M GILLESPIE 

 9113 LESAINT DR 

 FAIRFIELD OH 45014 

 2 MILLIKEN RESEARCH CORP 

 H KUHN 

 M MACLEOD 

 PO BOX 1926 

 SPARTANBURG SC 29303 

 1 CONNEAUGHT INDUSTRIES INC 

 J SANTOS 

 PO BOX 1425 

 COVENTRY RI 02816 

 1 ARMTEC DEFENSE PRODUCTS 

 S DYER 

 85 901 AVE 53 

 PO BOX 848 

 COACHELLA CA 92236 

 1 NATL COMPOSITE CTR 

 T CORDELL 

 2000 COMPOSITE DR 

 KETTERING OH 45420 

 3 PACIFIC NORTHWEST LAB 

 M SMITH 

 G VAN ARSDALE 

 R SHIPPELL 

 PO BOX 999 

 RICHLAND WA 99352 

 1 SAIC 

 M PALMER 

 1410 SPRING HILL RD STE 400 

 MS SH4 5 

 MCLEAN VA 22102 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

29

 1 ALLIANT TECHSYSTEMS INC 

 4700 NATHAN LN N 

 PLYMOUTH MN 55442-2512 

 1 APPLIED COMPOSITES 

 W GRISCH 

 333 NORTH SIXTH ST 

 ST CHARLES IL 60174 

 1 CUSTOM ANALYTICAL 

 ENG SYS INC 

 A ALEXANDER 

 13000 TENSOR LANE NE 

 FLINTSTONE MD 21530 

 1 AAI CORP 

 DR N B MCNELLIS 

 PO BOX 126 

 HUNT VALLEY MD 21030-0126 

 1 OFC DEPUTY UNDER SEC DEFNS 

 J THOMPSON 

 1745 JEFFERSON DAVIS HWY 

 CRYSTAL SQ 4 STE 501 

 ARLINGTON VA 22202 

 3 ALLIANT TECHSYSTEMS INC 

 J CONDON 

 E LYNAM 

 J GERHARD 

 WV01 16 STATE RT 956 

 PO BOX 210 

 ROCKET CENTER WV 

 26726-0210 

 1 PROJECTILE TECHNOLOGY INC 

 515 GILES ST 

 HAVRE DE GRACE MD 21078 

 1 HEXCEL INC 

 R BOE 

 PO BOX 18748 

 SALT LAKE CITY UT 84118 

 1 PRATT & WHITNEY 

 C WATSON 

 400 MAIN ST MS 114 37 

 EAST HARTFORD CT 06108 

 5 NORTHROP GRUMMAN 

 B IRWIN 

 K EVANS 

 D EWART 

 A SHREKENHAMER 

 J MCGLYNN 

 BLDG 160 DEPT 3700 

 1100 WEST HOLLYVALE ST 

 AZUSA CA 91701 

 1 HERCULES INC 

 HERCULES PLAZA 

 WILMINGTON DE 19894 

 1 BRIGS COMPANY 

 J BACKOFEN 

 2668 PETERBOROUGH ST 

 HERNDON VA 22071-2443 

 1 ZERNOW TECHNICAL SERVICES 

 L ZERNOW 

 425 W BONITA AVE STE 208 

 SAN DIMAS CA 91773 

 1 GENERAL DYNAMICS OTS 

 L WHITMORE 

 10101 NINTH ST NORTH 

 ST PETERSBURG FL 33702 

 2 GENERAL DYNAMICS OTS 

 FLINCHBAUGH DIV 

 K LINDE 

 T LYNCH 

 PO BOX 127 

 RED LION PA 17356 

 1 GKN WESTLAND AEROSPACE 

 D OLDS 

 450 MURDOCK AVE 

 MERIDEN CT 06450-8324 

 2 BOEING ROTORCRAFT 

 P MINGURT 

 P HANDEL 

 800 B PUTNAM BLVD 

 WALLINGFORD PA 19086 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

30

 5 SIKORSKY AIRCRAFT 

 G JACARUSO 

 T CARSTENSAN 

 B KAY 

 S GARBO MS S330A 

 J ADELMANN 

 6900 MAIN ST 

 PO BOX 9729 

 STRATFORD CT 06497-9729 

 1 AEROSPACE CORP 

 G HAWKINS M4 945 

 2350 E EL SEGUNDO BLVD 

 EL SEGUNDO CA 90245 

 2 CYTEC FIBERITE 

 M LIN 

 W WEB 

 1440 N KRAEMER BLVD 

 ANAHEIM CA 92806 

 2 UDLP 

 G THOMAS 

 M MACLEAN 

 PO BOX 58123 

 SANTA CLARA CA 95052 

 1 UDLP WARREN OFC 

 A LEE 

 31201 CHICAGO RD SOUTH 

 SUITE B102 

 WARREN MI 48093 

 2 UDLP 

 R BRYNSVOLD 

 P JANKE MS 170 

 4800 EAST RIVER RD 

 MINNEAPOLIS MN 55421-1498 

 1 LOCKHEED MARTIN 

 SKUNK WORKS 

 D FORTNEY 

 1011 LOCKHEED WAY 

 PALMDALE CA 93599-2502 

 1 LOCKHEED MARTIN 

 R FIELDS 

 5537 PGA BLVD 

 SUITE 4516 

 ORLANDO FL 32839 

 1 NORTHRUP GRUMMAN CORP 

 ELECTRONIC SENSORS 

 & SYSTEMS DIV 

 E SCHOCH MS V 16 

 1745A W NURSERY RD 

 LINTHICUM MD 21090 

 1 GDLS DIVISION 

 D BARTLE 

 PO BOX 1901 

 WARREN MI 48090 

 2 GDLS 

 D REES 

 M PASIK 

 PO BOX 2074 

 WARREN MI 48090-2074 

 1 GDLS 

 MUSKEGON OPER 

 M SOIMAR 

 76 GETTY ST 

 MUSKEGON MI 49442 

 1 GENERAL DYNAMICS 

 AMPHIBIOUS SYS 

 SURVIVABILITY LEAD 

 G WALKER 

 991 ANNAPOLIS WAY 

 WOODBRIDGE VA 22191 

 6 INST FOR ADVANCED 

 TECH 

 H FAIR 

 I MCNAB 

 P SULLIVAN 

 S BLESS 

 W REINECKE 

 C PERSAD 

 3925 W BRAKER LN STE 400 

 AUSTIN TX 78759-5316 

 1 ARROW TECH ASSOC 

 1233 SHELBURNE RD STE D8 

 SOUTH BURLINGTON VT 

 05403-7700 

 1 R EICHELBERGER 

 CONSULTANT 

 409 W CATHERINE ST 

 BEL AIR MD 21014-3613 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

31

 1 SAIC 

 G CHRYSSOMALLIS 

 8500 NORMANDALE LAKE BLVD 

 SUITE 1610 

 BLOOMINGTON MN 55437-3828 

 1 UCLA MANE DEPT ENGR IV 

 H T HAHN 

 LOS ANGELES CA 90024-1597 

 2 UNIV OF DAYTON 

 RESEARCH INST 

 R Y KIM 

 A K ROY 

 300 COLLEGE PARK AVE 

 DAYTON OH 45469-0168 

 1 UMASS LOWELL 

 PLASTICS DEPT 

 N SCHOTT 

 1 UNIVERSITY AVE 

 LOWELL MA 01854 

 1 IIT RESEARCH CTR 

 D ROSE 

 201 MILL ST 

 ROME NY 13440-6916 

 1 GA TECH RESEARCH INST 

 GA INST OF TCHNLGY 

 P FRIEDERICH 

 ATLANTA GA 30392 

 1 MICHIGAN ST UNIV 

 MSM DEPT 

 R AVERILL 

 3515 EB 

 EAST LANSING MI 48824-1226 

 1 UNIV OF WYOMING 

 D ADAMS 

 PO BOX 3295 

 LARAMIE WY 82071 

 1 PENN STATE UNIV 

 R S ENGEL 

 245 HAMMOND BLDG 

 UNIVERSITY PARK PA 16801 

 2 PENN STATE UNIV 

 R MCNITT 

 C BAKIS 

 212 EARTH ENGR 

 SCIENCES BLDG 

 UNIVERSITY PARK PA 16802 

 1 PURDUE UNIV 

 SCHOOL OF AERO & ASTRO 

 C T SUN 

 W LAFAYETTE IN 47907-1282 

 1 STANFORD UNIV 

 DEPT OF AERONAUTICS 

 & AEROBALLISTICS 

 S TSAI 

 DURANT BLDG 

 STANFORD CA 94305 

 1 UNIV OF MAINE 

 ADV STR & COMP LAB 

 R LOPEZ ANIDO 

 5793 AEWC BLDG 

 ORONO ME 04469-5793 

 1 JOHNS HOPKINS UNIV 

 APPLIED PHYSICS LAB 

 P WIENHOLD 

 11100 JOHNS HOPKINS RD 

 LAUREL MD 20723-6099 

 1 UNIV OF DAYTON 

 J M WHITNEY 

 COLLEGE PARK AVE 

 DAYTON OH 45469-0240 

 1 NORTH CAROLINA ST UNIV 

 CIVIL ENGINEERING DEPT 

 W RASDORF 

 PO BOX 7908 

 RALEIGH NC 27696-7908 

 5 UNIV OF DELAWARE 

 CTR FOR COMPOSITE MTRLS 

 J GILLESPIE 

 M SANTARE 

 S YARLAGADDA 

 S ADVANI 

 D HEIDER 

 201 SPENCER LAB 

 NEWARK DE 19716 
NO. OF NO. OF 

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32

 1 DEPT OF MTRLS 

 SCIENCE & ENGRG 

 UNIV OF ILLINOIS 

 AT URBANA CHAMPAIGN 

 J ECONOMY 

 1304 WEST GREEN ST 115B 

 URBANA IL 61801 

 1 UNIV OF MARYLAND 

 DEPT OF AEROSPACE ENGRG 

 A J VIZZINI 

 COLLEGE PARK MD 20742 

 1 DREXEL UNIV 

 A S D WANG 

 3141 CHESTNUT ST 

 PHILADELPHIA PA 19104 

 3 UNIV OF TEXAS AT AUSTIN 

 CTR FOR ELECTROMECHANICS 

 J PRICE 

 A WALLS 

 J KITZMILLER 

 10100 BURNET RD 

 AUSTIN TX 78758-4497 

 3 VA POLYTECHNICAL 

 INST & STATE UNIV 

 DEPT OF ESM 

 M W HYER 

 K REIFSNIDER 

 R JONES 

 BLACKSBURG VA 24061-0219 

 1 SOUTHWEST RESEARCH INST 

 ENGR & MATL SCIENCES DIV 

 J RIEGEL 

 6220 CULEBRA RD 

 PO DRAWER 28510 

 SAN ANTONIO TX 78228-0510 

 1 BATELLE NATICK OPERS 

 B HALPIN 

 313 SPEEN ST 

 NATICK MA 01760 

 3 DIRECTOR 

 US ARMY RESEARCH LAB 

 AMSRD ARL WM MB 

 A FRYDMAN 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

ABERDEEN PROVING GROUND

 1 US ARMY ATC 

 CSTE DTC AT AC I 

 W C FRAZER 

 400 COLLERAN RD 

 APG MD 21005-5059 

 91 DIR USARL 

 AMSRD ARL CI 

 AMSRD ARL O AP EG 

 M ADAMSON 

 AMSRD ARL SL BA 

 AMSRD ARL SL BB 

 D BELY 

 AMSRD ARL WM 

 J SMITH 

 H WALLACE 

 AMSRD ARL WM B 

 A HORST 

 T KOGLER 

 AMSRD ARL WM BA 

 D LYON 

 AMSRD ARL WM BC 

 J NEWILL 

 P PLOSTINS 

 A ZIELINSKI 

 AMSRD ARL WM BD 

 P CONROY 

 B FORCH 

 M LEADORE 

 C LEVERITT 

 R LIEB 

 R PESCE RODRIGUEZ 

 B RICE 

 AMSRD ARL WM BF 

 S WILKERSON 

 AMSRD ARL WM M 

 B FINK 

 J MCCAULEY 

 AMSRD ARL WM MA 

 L GHIORSE 

 S MCKNIGHT 

 E WETZEL 

 AMSRD ARL WM MB 

 J BENDER 

 T BOGETTI 

 L BURTON 

 R CARTER 

 K CHO 

 W DE ROSSET 

 G DEWING 

 R DOWDING 

 W DRYSDALE 
NO. OF NO. OF 

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 R EMERSON 

 D HENRY 

 D HOPKINS 

 R KASTE 

 L KECSKES 

 M MINNICINO 

 B POWERS 

 D SNOHA 

 J SOUTH 

 M STAKER 

 J SWAB 

 J TZENG 

 AMSRD ARL WM MC 

 J BEATTY 

 R BOSSOLI 

 E CHIN 

 S CORNELISON 

 D GRANVILLE 

 B HART 

 J LASALVIA 

 J MONTGOMERY 

 F PIERCE 

 E RIGAS 

 W SPURGEON 

 AMSRD ARL WM MD 

 B CHEESEMAN 

 P DEHMER 

 R DOOLEY 

 G GAZONAS 

 S GHIORSE 

 C HOPPEL 

 M KLUSEWITZ 

 W ROY 

 J SANDS 

 D SPAGNUOLO 

 S WALSH 

 S WOLF 

 AMSRD ARL WM RP 

 J BORNSTEIN 

 C SHOEMAKER 

 AMSRD ARL WM T 

 B BURNS 

 AMSRD ARL WM TA 

 W BRUCHEY 

 M BURKINS 

 W GILLICH 

 B GOOCH 

 T HAVEL 

 E HORWATH 

 M NORMANDIA 

 J RUNYEON 

 M ZOLTOSKI 

 AMSRD ARL WM TB 

 P BAKER 

 AMSRD ARL WM TC 

 R COATES 

 AMSRD ARL WM TD 

 D DANDEKAR 

 T HADUCH 

 T MOYNIHAN 

 M RAFTENBERG 

 S SCHOENFELD 

 T WEERASOORIYA 

 AMSRD ARL WM TE 

 A NIILER 

 J POWELL 
NO. OF NO. OF 

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 1 LTD 

 R MARTIN 

 MERL 

 TAMWORTH RD 

 HERTFORD SG13 7DG 

 UK 

 1 SMC SCOTLAND 

 P W LAY 

 DERA ROSYTH 

 ROSYTH ROYAL DOCKYARD 

 DUNFERMLINE FIFE KY 11 2XR 

 UK 

 1 CIVIL AVIATION 

 ADMINSTRATION 

 T GOTTESMAN 

 PO BOX 8 

 BEN GURION INTRNL AIRPORT 

 LOD 70150 

 ISRAEL 

 1 AEROSPATIALE 

 S ANDRE 

 A BTE CC RTE MD132 

 316 ROUTE DE BAYONNE 

 TOULOUSE 31060 

 FRANCE 

 1 DRA FORT HALSTEAD 

 P N JONES 

 SEVEN OAKS KENT TN 147BP 

 UK 

 1 SWISS FEDERAL ARMAMENTS 

 WKS 

 W LANZ 

 ALLMENDSTRASSE 86 

 3602 THUN 

 SWITZERLAND 

 1 DYNAMEC RESEARCH LAB 

 AKE PERSSON 

 BOX 201 

 SE 151 23 SODERTALJE 

 SWEDEN 

 1 ISRAEL INST OF TECHLGY 

 S BODNER 

 FACULTY OF MECHANICAL 

 ENGR 

 HAIFA 3200 

 ISRAEL 

 1 DSTO 

 WEAPONS SYSTEMS DIVISION 

 N BURMAN RLLWS 

 SALISBURY 

 SOUTH AUSTRALIA 5108 

 AUSTRALIA 

 1 DEF RES ESTABLISHMENT 

 VALCARTIER 

 A DUPUIS 

 2459 BLVD PIE XI NORTH 

 VALCARTIER QUEBEC 

 CANADA 

 PO BOX 8800 COURCELETTE 

 GOA IRO QUEBEC 

 CANADA 

 1 ECOLE POLYTECH 

 J MANSON 

 DMX LTC 

 CH 1015 LAUSANNE 

 SWITZERLAND 

 1 TNO DEFENSE RESEARCH 

 R IJSSELSTEIN 

 ACCOUNT DIRECTOR 

 R&D ARMEE 

 PO BOX 6006 

 2600 JA DELFT 

 THE NETHERLANDS 

 2 FOA NATL DEFENSE RESEARCH 

 ESTAB 

 DIR DEPT OF WEAPONS & 

 PROTECTION 

 B JANZON 

 R HOLMLIN 

 S 172 90 STOCKHOLM 

 SWEDEN
NO. OF 

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 2 DEFENSE TECH & PROC 

 AGENCY GROUND 

 I CREWTHER 

 GENERAL HERZOG HAUS 

 3602 THUN 

 SWITZERLAND 

 1 MINISTRY OF DEFENCE 

 RAFAEL 

 ARMAMENT DEVELOPMENT 

 AUTH 

 M MAYSELESS 

 PO BOX 2250 

 HAIFA 31021 

 ISRAEL 

 1 TNO DEFENSE RESEARCH 

 I H PASMAN 

 POSTBUS 6006 

 2600 JA DELFT 

 THE NETHERLANDS 

 1 B HIRSCH 

 TACHKEMONY ST 6 

 NETAMUA 42611 

 ISRAEL 

 1 DEUTSCHE AEROSPACE AG 

 DYNAMICS SYSTEMS 

 M HELD 

 PO BOX 1340 

 D 86523 SCHROBENHAUSEN 

 GERMANY 
36

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