Numerical Hopkinson Bar Analysis: Uni-Axial Stress and 

Planar Bar-Specimen Interface Conditions by Design 

by Bazle A. Gama and John W. Gillespie, Jr. 

ARL-CR-553 September 2004 

prepared by 

University of Delaware 

Center for Composite Materials 

Newark, DE 19716 

under contract 

DAAD19-01-2-0005 

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

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ARL-CR-553 September 2004 

Numerical Hopkinson Bar Analysis: Uni-Axial Stress and 

Planar Bar-Specimen Interface Conditions by Design 

Bazle A. Gama and John W. Gillespie, Jr. 

University of Delaware 

Center for Composite Materials 

Newark, DE 19716 

prepared by 

University of Delaware 

Center for Composite Materials 

Newark, DE 19716 

under contract 

DAAD19-01-2-0005 

Approved for public release; distribution is unlimited.
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Numerical Hopkinson Bar Analysis: Uni-Axial Stress and Planar Bar-Specimen 

Interface Conditions by Design 

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Bazle A. Gama* and John W. Gillespie, Jr.* 

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University of Delaware 

Center for Composite Materials 

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*University of Delaware, Center for Composite Materials, Newark, DE 19716 

14. ABSTRACT 

High strain rate characterization of materials is usually performed using the Split Hopkinson Pressure Bar (SHPB) in the strain

rate range, 2 4 10 – 10 . < In the one-dimensional analysis of Hopkinson bar experiment, it is assumed that the specimen 

deforms under uni-axial stress, the bar-specimen interfaces remain planar at all-time, and the stress equilibrium in the specimen 

is achieved in travel times. The first two assumptions are in general not true for acoustically hard specimens with diameter 

smaller than the bars. Explicit dynamic finite element analyses are used to investigate these assumptions. A new specimen 

design is suggested which satisfies the uni-axial stress condition in the specimen under the linear-elastic deformation phase of 

the specimen. A new Hopkinson bar experimental technique is presented to ensure that the bar-specimen interfaces remain 

planar at all time. Extensive numerical analyses are performed to quantify the accuracy of the proposed configurations. 

15. SUBJECT TERMS

SHPB, numerical simulation, 3-D analysis, uni-axial stress, specimen design, planar bar-specimen interface, transmission tube 

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iii

Contents 

List of Figures iv

List of Tables v

Acknowledgments vi

1. Introduction 1

1.1 SHPB Specimen Design....................................................................................................1 

1.1.1 Specimen Design to Minimize Friction and Inertia ..............................................2 

1.1.2 Experimental Study on Specimen Shape and Failure ...........................................4 

1.2 Objectives..........................................................................................................................6 

2. Numerical Simulation of Compression SHPB Experiment 6

3. Effect of Nonplanar Bar-Specimen Interface: The Problem 9

4. Uni-Axial Stress Along the Specimen Through Specimen Design: Partial Solution 10

4.1 Specimen Design 1: Cylindrical Specimen With Chamfered Edges..............................11 

4.2 Specimen Design 2: Dog Bone/Dumbbell-Shaped Cylindrical Specimen.....................15 

5. Planar Bar-Specimen Interface Condition Through Experiment Design: Complete 

Solution 19

5.1 Compression SHPB With a TT .......................................................................................19 

5.2 Numerical Simulation of Compression SHPB With TT .................................................22 

6. Summary 30

7. References 31

Distribution List 35 
iv

List of Figures 

Figure 1. Damage at the impact end of Takeda’s unidirectional specimen at different loading 

levels. .........................................................................................................................................4 

Figure 2. Dog bone-shaped hollow cylindrical specimen geometry for torsional testing. .............5 

Figure 3. New compression SHPB specimen geometry proposed by Deltort et al. All 

dimensions in millimeters..........................................................................................................5 

Figure 4. Schematic diagram of a compression SHPB and the notations used in the analyses......7 

Figure 5. Quartersymmetric model of SHPB and finite element mesh. .........................................7 

Figure 6. Loading history on the impact face of the IB..................................................................9 

Figure 7. Nonplanar bar-specimen interface deformation model of a small diameter hard 

specimen: j

i u – axial displacements in Z-direction; subscripts i = C, D, and E represent 

bar-center, specimen-edge, and bar-edge, respectively; superscripts j = 1 and 2; 

“1” = IB-S interface; “2” = S-TB interface..............................................................................10 

Figure 8. Numerical Hopkinson bar responses for two different test cases..................................11 

Figure 9. Contours of axial stress distribution in the specimen at a different time. .....................12 

Figure 10. Quartersymmetric finite element model of Hopkinson bars and cylindrical 

ceramic specimen with chamfered edges, D / D = 0.60 , S B H / D 1.00 S S = , S D = 0.60. ˆ .........13 

Figure 11. Axial stress distribution on the surface of ceramic specimen at a different time, ˆt t/T = , S D 0.60 ˆ = , r / R 1.00 = , Max

Z IB max P 500 σ= = − MPa.....................................................13 

Figure 12. Distribution of dimensionless axial stress along the length of a cylindrical 

specimen with and without chamfered edges. .........................................................................14 

Figure 13. Distribution of axial stress in the radial direction at different Z / H locations of a 

cylindrical specimen with chamfered edges, ˆt t / T 0.25. = = ..................................................15 

Figure 14. The parametric definition of a cylindrical dog bone/dumbbell-shaped specimen 

proposed by Deltort et al..........................................................................................................16 

Figure 15. Contours of axial stress distribution in the dog bone-shaped specimen at a 

different time............................................................................................................................17 

Figure 16. Distribution of dimensionless axial stress along the length of a dog bone-shaped 

specimen and that for cylindrical specimens with and without chamfered edges. ..................18 

Figure 17. Deviation from stress equilibrium of different specimen designs...............................18 

Figure 18. A new compression SHPB experimental set-up with TT............................................20 

Figure 19. Finite element model of the compression SHPB with TT...........................................22 

Figure 20. Bar responses of the new compression SHPB with TT...............................................24 

Figure 21. Notations for axial displacements measured at different radial locations of 

different bars. ...........................................................................................................................24 

Figure 22. Nonplanar interface parameter, i u , as a function of time, ceramic specimen. ...........25 ˆ
v

Figure 23. Nonplanar interface parameter, i u , as a function of time, aluminum specimen.........25 ˆ

Figure 24. HPB with TT: applications with direct impact and hollow cylindrical specimen......28 

Figure 25. Deviation from the stress equilibrium of the ceramic specimen with a different HS

/ DS ratio, SHPB with TT.........................................................................................................29

Figure 26. Stress-strain response of SHPB with TT and comparison with classic methods, HS

/ DS, DS / DIB = 0.60.................................................................................................................30 

List of Tables 

Table 1. Geometric properties of the SHPB. ..................................................................................8 

Table 2. Linear-elastic and elastic-plastic material constants.........................................................8 

Table 3. Nonplanar bar-specimen interface parameters and fitting constants for ceramic 

specimen and steel bars............................................................................................................26 

Table 4. Nonplanar bar-specimen interface parameters and fitting constants for the 

aluminum specimen and steel bars. .........................................................................................27 
vi

Acknowledgments 

This report is prepared through participation in the Composite Materials Technology 

Collaborative Program sponsored by the U.S. Army Research Laboratory under Cooperative 

Agreement DAAD19-01-2-0005. The authors gratefully acknowledge the help provided by 

Dr. Libo Ren in data reduction, using the dispersion correction software “Hopkinson” developed 

by himself and coworkers at the University of Delaware-Center for Composite Materials. 

Discussion and difference in opinion with Dr. Sergey L. Lopatnikov generated new ideas of 

Hopkinson bar experiments and analysis, and is gratefully acknowledged.
1 

1. Introduction 

Hopkinson bar experimental techniques (1–5) are considered the simplest high strain rate test 

method compared to plate impact (4) and explosive loading techniques (4, 6). Significant 

advances have been made in the Hopkinson Bar research field to accommodate new test methods 

(7–9) and new analyses techniques (10, 11). A recent critical review by the authors elucidating 

the 20th century advancement in Hopkinson bar techniques (12) pointed out some further areas 

that need improvement prior to becoming a standard test method. Two such areas are considered 

in the present study: the specimen deforming under uni-axial stress and the bar-specimen 

interfaces remaining planar throughout the duration of the test. 

Finite element analysis (FEA) has been performed to study the validity of one-dimensional (1-D) 

assumptions (13) of compression split-Hopkinson Pressure Bar (SHPB) technique. It has been 

identified that the nonplanar bar-specimen assumption made in Hopkinson Bar analysis is not 

valid for an acoustically hard specimen with diameter smaller than the bar. As a consequence, 

the average strain of the specimen measured from the bar response is found unreliable. The axial 

stress distribution of the specimen is found to be nonuniform in the linear elastic phase of 

deformation; however, it is uniform in the plastic phase. It has been identified that the stress 

equilibrium in an elastic-plastic specimen is not achieved in the linear elastic phase of 

deformation; however, the deviation from equilibrium in the plastic deformation phase is 

constant and minimum but not absolutely zero. These important observations focused our efforts 

on identifying mechanisms to achieve uni-axial stress via design of the specimen geometry while 

simultaneously minimizing the nonplanar deformation of the bar-specimen interfaces via 

modifications to the test fixturing. Our objective is to achieve more accurate strain 

measurements enabling high strain rate properties in the elastic regime to be measured reliably. 

1.1 SHPB Specimen Design 

Historically, right circular cylindrical specimens have been used in the compression testing of 

isotropic elastic-plastic materials. However, researchers have looked at many different specimen 

geometries while conducting tension, shear, and torsion testing of materials under Hopkinson bar 

loading (4). Top hat specimen geometry for measuring tension properties using the compression 

SHPB is described by Lindholm and Yeakley (14). Dog bone-shaped cylindrical (15, 16) and 

strip specimens (17–20) have been used in tension split SHPB testing. A double-notch-shear 

(DNS) testing (21) and punch loading (22) are described in reference (4), where an incident bar 

and a transmitter tube are used in conjunction with double-notch and flat-plate specimens. 

A hat-shaped specimen can also be used with traditional SHPB for shear testing (4). 

Dog bone-shaped tubular specimens, on the other hand, are generally used for torsion testing 

(23) at high loading rates.
2 

1.1.1 Specimen Design to Minimize Friction and Inertia 

Specimen design with the objectives of minimizing friction and inertia effects has also been 

looked at in the past by many researchers. The maximum specimen diameter ( D ) that can be S

allowed is equal to the bar diameter (D ). Gray ( B 24) suggested that the radial and longitudinal 

inertia and friction effects can be lessened by minimizing the areal-mismatch between the bar 

and specimen ( D ~ 0.80D ); and choosing S B H /D ratio ( S S H – length of the specimen) between S

0.50 and 1.0, which is based on the corrections for inertia effects proposed by Davies and Hunter 

(25): 

( ) ( ) ( ) CM 2 2 2 2 σS S S S SS (t) = σ (t) + ρ ⎡ ⎤ H 6– ν D8× ∂ ε (t) t ∂ ⎣ ⎦ , (1) 

where subscript S stands for “specimen,” and superscripts C and M stand for “corrected” and 

“measured,” respectively. This expression predicts that the correction term will be zero, if either 

the strain rate is constant or the bracketed term is zero. The later condition provides the optimum 

ratio of the specimen for inertia effect and is expressed as follows: 

H /D = 3v /4 (2) SS S

For a Poisson’s ratio of 0.333, the optimum H / D is 0.50. To minimize the friction effects, the S S

H / D ratio should be in the range 1.50–2.00 ( S S 26). Thus the conditions for minimum friction 

and inertia effects cannot be satisfied simultaneously and Gray’s (24) suggestion of 

0.50 < H / D < 1.0 can be taken as a compromise between these two effects. S S

If a constant strain rate condition is used, then one can effectively use thinner specimens 

( H / D < 0.50), and thus minimize the stress nonequilibrium in the specimen. Usually, S S

constant strain rate conditions can be achieved through shaped incident pulses; however, the 

attainable strain rates in these cases are limited by the stress rate of the incident pulse (27). The 

optimum thickness of the specimen depends on the rise time, t, required to achieve a uni-axial 

stress state in the specimen. The rise time is estimated as the time required for π reverberations 

in the specimen (26). For a plastically deforming solid that obeys the Taylor-von Karman 

Theory, the rise time is given by 

2 22

S S t ( H )/( / ) ≥ π ρ ∂σ ∂ε , (3) 

where ρS and H are the density and thickness of the specimen, respectively, and S ∂σ ∂ε / is the 

stage 2 work-hardening rate of the true stress-strain diagram of the material to be tested. By 

decreasing the specimen thickness, it is thus possible to reduce the rise time; however, the 

specimen H / D requirement for minimizing friction a S S nd inertia effects requires that the 

specimen diameter also be reduced. Consequently, one needs to use a smaller diameter bar as 

well (to satisfy the conditions, DS ~ 0.80DB and 0.50 < H / D < 1.0). S S
3 

Malinowski and Klepaczko (28) presented a combined analytical, experimental and numerical 

study in the determination of an optimum specimen geometry used in the SHPB test technique. 

In addition to specimen inertia investigated by Davies and Hunter (25), the effect of interfacial 

friction between the Hopkinson bars and a cylindrical specimen is considered in the analysis. A 

unified approach to inertia and friction is offered through the consideration of energy balance. 

The difference between the measured ( M σS ) and correct ( C σS ) specimen stress using “3-wave” 

analysis can be expressed as follows: 

( ) ( )

2 M 2

MC 2 2 S SS S

S S S S

SS S

D H 3 3 D

3 H / D 12 D 16 64

⎡ ⎤ μσ ρ ⎛ ⎞

σ −σ = + − ⋅ ε +ε + ρ ε ⎢ ⎥ ⎜ ⎟ ⋅ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦

  , (4) 

where μ is the coefficient of Coulomb friction, and both H and S D represent their respective S

instantaneous values. If the optimum value H / D is sought by setting, S S

M C

S S σ −σ = 0 , then the 

following solution is obtained: 

( ) ( ) ( )

1

3 M 1 1

S S 3 3

2 2 S Opt S S

H 2 11 11

D D

⎡ ⎤ ⎛ ⎞ ⋅μσ ⎡ ⎤ =− ⋅ − +β + + +β ⎢ ⎥ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎢ ⎥ ρ ⋅ ε +ε ⎣ ⎦ ⎣ ⎦  

, 

and 

( )

( )

2 3 2

S S

M 2

S

D 0.5

16 8

⎛ ⎞ ρ ε − ε β= ⋅ ⎜ ⎟

⋅μσ ⋅ ⎝ ⎠ ε + ε

 

 

. (5) 

While the detailed analysis of equations 4 and 5 can be found in reference (28), the major 

conclusions about the optimum specimen H / D ratio are summarized here. The optimum S S

H / D is a function of coefficient of friction, sp S S ecimen stress, density, strain rate, and strain 

acceleration. Thus, there is no universal optimum H / D ratio, rather it changes with S S ε and ε

of the test for a given specimen material. Based on the fact that the optimum H / D ratio is a S S

function of M

S S σ ρ/ of the specimen, Malinowski and Klepaczko (28) identified three ranges of 

optimum H / D values for metals: S S

1. For materials with high M

S S σ ρ/ ratio (e.g., titanium, high-strength steel, etc.) – 

S S 1.0 H / D 1.5 ≤ ≤ . 

2. For materials with medium M

S S σ ρ/ ratio (e.g., aluminum, copper, etc.) – 

S S 0.5 H / D 1.0 ≤ ≤ . 

3. For materials with low M

S S σ ρ/ ratio (e.g., lead, gold, etc.) – S S 0.1 H / D 0.5 ≤ ≤ . 

In addition to the previously mentioned discussion on the optimum H / D ratio for metallic S S

specimens, there are additional guidelines for soft (29) and hard (27) specimens also. 

Chen et al. (30) observed substantial wave attenuation in thick (0.25-in) RTV630 rubber samples 
4 

as compared with thin (0.06-in) samples, suggesting that depending on test temperature and 

specimen material, an H / D ratio of 0.25–0.50 can be used to minimize attenuation. Ceramic S S

specimens, on the other hand, possess high-failure strength and relatively low-failure strain. In 

order to allow sufficient deformation of the specimen before failure, the recommended H /D S S

ratio for ceramic specimens is usually higher than for the metallic specimens 

( S S 1.0 H / D 2.0 < < ) (27). 

1.1.2 Experimental Study on Specimen Shape and Failure 

Harding (31) used waisted strip specimen (in-plane shape is rectangular and dog bone shaped 

through the thickness) under compression SHPB technique and found that stress equilibrium is 

hard to achieve. On the other hand, Harding’s compression SHPB experiments on cylindrical 

specimens with specimen length to diameter ratio, H / D = 1.0, 2.0, and 2.5 in the warp and S S

weft directions revealed that in addition to the shear band formation, specimens with higher 

H / D ratio introduce longitudinal spli S S tting as an additional failure mode. 

Takeda and Wan (32) tested unidirectional glass/polyester specimens with square cross section in 

the fiber direction and studied the evolution of specimen damage as a function of loading level 

controlled via a recovery SHPB. Figure 1 shows the damage at the impact end at three different 

load levels. Clearly, the stress concentration developed at the edges and corners of the specimen 

due to the nonplanar bar-specimen interface deformation initiated damage at those locations; and 

as the load is increased, the loci of failure progressed radially inward. 

Figure 1. Damage at the impact end of Takeda’s unidirectional specimen at different loading levels.*

Leber and Lifshitz (33) used dog bone-shaped hollow cylindrical specimens (figure 2) for 

torsional testing of plain-weave E-glass/epoxy composite materials; however, results from 

dynamic finite element analysis showed that the shear stress distribution is not uniform in the 

gage section of the specimen. 

Deltort et al. (34) pointed out the importance of friction, elastic punching, and parasitic bending 

on the results of static and SHPB compression tests with standard cylindrical specimens in their 

brief article. They described that any imperfect contact between specimen and loading interfaces 

and the misalignment between the specimen and loading axes are the causes of specimen 

bending. Through quasi-static experiments and finite element modeling, they identified the fact 

 *

 Figure 1 is a reproduction taken from reference (32), figure 7, p 112. 
5 

Figure 2. Dog bone-shaped hollow cylindrical 

specimen geometry for torsional testing.*

that friction between specimen and interfaces and elastic punching effect lead to a heterogeneous 

state of specimen strain and can cause barreling of the specimen at large deformation. A new 

specimen design is proposed, which has a dog bone/dumbbell shape (figure 3). They performed 

a few quasi-static and SHPB compression experiments to prove the concept. The new specimen 

is found to have a problem of buckling because of its longer length. 

Figure 3. New compression SHPB specimen geometry proposed by 

Deltort et al.† All dimensions in millimeters. 

Ninan et al. (35) used both two-dimensional (2-D) plane stress and an axisymmetric model of the 

full SHPB and studied the effect of interface friction and incident pulse shape. The strain history 

of a rectangular specimen (axial dimension smaller than bar diameter) was presented at five 

different points, considering both frictionless and constrained boundaries. The strain 

history/distribution was found uniform for the frictionless case, but nonuniform for the 

constrained case. A conclusion was made that friction at bar-specimen interfaces may produce 

nonhomogeneous strain distribution in the specimen.

 *

Figure 2 is a reproduction taken from reference (33), figure 3, p 394. 

†

 Figure 3 is a reproduction taken from reference (34), figure 3, p C3–267. 
6 

1.2 Objectives 

Earlier works considered the SHPB specimen design to minimize friction and inertia (radial and 

axial) through theoretical and numerical analyses. Bertholf and Karnes (36) described the first 

comprehensive 2-D numerical analysis of compression SHPB. A brief review of numerical 

Hopkinson Bar modeling can be found in reference (13). A more recent numerical study by 

Zencker and Clos (37) has identified that “in the initial state of a SHPB test, the specimen 

behaves elastically with high stress triaxiality. In this early phase, the results of the SHPB 

procedure are inaccurate. They can be improved by well-known inertia corrections, but error 

remains.” The objectives of the present study are different than what has been addressed by 

other researchers. In this study, specimen designs are presented which will improve the uni-axial 

stress state in the specimen in the elastic phase of deformation. In addition, the new 

experimental technique is presented which minimizes the planar bar-specimen interface 

deformation and thereby reduces the error in the measurement of average specimen strain using 

one-dimensional (1-D) Hopkinson bar analysis. New concepts of specimen and experiment 

designs are analyzed using a three-dimensional (3-D) finite element model of compression SHPB 

apparatus. All numerical simulations of compression SHPB experiment are performed using 

dynamic explicit Lagrangian hydrocode LS-DYNA 960. 

2. Numerical Simulation of Compression SHPB Experiment 

A traditional compression SHPB consists of two bars of equal length and diameter, and is known 

as incident/input bar (IB) and transmitter/output bar (TB). A striker bar (SB) impacts the impact 

end of the IB, while the specimen (S, SP) in the form of a right circular cylinder is sandwiched in 

between the IB and TB (figure 4a). The impact of a projectile produces a compression 

stress/strain pulse, which propagates along the bar and loads the specimen under compression. A 

part of the incident pulse reflects back from the incident bar-specimen (IB-S) interface and a part 

is transmitted to the TB through the specimen-transmitter bar (S-TB) interface. The incident 

( I ε (t) ), reflected ( Rε (t)), and transmitted ( T ε (t) ) pulses are recorded through the strain gages 

(SGs) mounted at the midlength on the bar surfaces, and are used to calculate the average stress 

and strain of the specimen following the 1-D Hopkinson Bar analysis (24). 

In a previous study (13), a quartersymmetric finite element model of a compression SHPB was 

developed in three dimensions. A mesh sensitivity analysis along the length (Z-axis) was 

performed to identify the minimum number of elements necessary to obtain convergence, and 

400 elements were found sufficient to predict the Hopkinson bar experimental responses. The 

accuracy of the numerical model was verified by simulating the 1-D stress wave propagation in a 

long rod with free and fixed boundary conditions. The contact modeling between bar-specimen 

and bar-bar interfaces was verified by computing the reflection coefficients from an interface 

with unequal cross sections. The impact-contact of an SB on the IB was verified by computing 
7 

the stress in the bar, particle velocities of the propagating stress waves, and the duration of pulses 

as a function of SB lengths. The finite diameter effect in an SHPB was evaluated by the study of 

shaped pulses. The model was also validated for a “bars together” calibration experiment. The 

model was found to predict all the previously mentioned analytical problems with sufficient 

accuracy. This well-verified and validated model is used in the present analyses. The axis of the 

cylindrical specimen is taken as the Z-axis, and the axis orthogonal to the Z-axis is taken as the 

radial axis, r (also X and Y axes [figure 4b]). The details of the model can be found in reference 

(13). For completeness, a brief summary is presented next. 

Figure 4. Schematic diagram of a compression SHPB and the notations used in the analyses. 

A 3-D model of the SHPB is developed using 8-node solid elements. A 1-point integration 

scheme is used to save computational time. The longitudinal axis of the bars is taken as the 

geometric Z-axis. In the case of a specimen with a circular or rectangular cross section, two 

planes of symmetry passing through X-Z and Y-Z plane exist. In the present study, a 

quartersymmetric model (figure 5) with appropriate boundary conditions in the symmetric planes 

is used. The impact velocity of the SB is used as the initial condition, or a pressure pulse is 

applied on the impact face of the IB. A surface-to-surface contact interface condition without 

friction is defined between the bar interfaces. The specimen in the form of a right circular 

cylinder or a dog bone/dumbbell shape is considered. 

Figure 5. Quartersymmetric model of SHPB and finite element mesh.

Striker Bar

(SB)

Incident/Input Bar

(IB)

Transmitter/Output Bar

(TB)

Specimen

(SP)

Strain Gage (SG) Strain Gage

Striker Bar

(SB)

Incident/Input Bar

(IB)

Transmitter/Output Bar

(TB)

Specimen

(SP)

Strain Gage (SG) Strain Gage

H

Z

r, X, Y

R

0

(a) Compression SHPB (b) Notations 

Transmission Bar 

(TB) 

Striker Bar 

(SB)

Incident Bar 

(IB)

Specimen 

(SP)

Transmission Bar 

(TB) 

Striker Bar 

(SB)

Incident Bar 

(IB)

Specimen 

(SP)
8 

The geometric dimensions of the model are presented in table 1; however, all of these 

dimensions can be varied as a test parameter. The bars remain elastic at all times during the 

SHPB experiment, and thus a linear-elastic isotropic material model is considered for the bars. 

The specimens are modeled with both linear-elastic and elastic-plastic isotropic material models. 

Two material parameters, Young’s modulus (E) and Poisson’s ratio (ν), are required to describe 

a linear-elastic model; however, two additional parameters, yield stress (σy) and tangent modulus 

(Et), are necessary for elastic-plastic definition. For wave propagation analysis, density (ρ) of 

the material is also necessary. The material properties used in the numerical simulation are listed 

in table 2 including the calculated bar velocity C E/ 0 = ρ . 

Table 1. Geometric properties of the SHPB. 

Parameter SB IB TB SP 

Length (mm) 304.80 1524 1524 Variable 

Diameter (mm) 25.40 25.40 25.40 Variable 

Table 2. Linear-elastic and elastic-plastic material constants. 

Material Ρ

(g/cm3) 

E 

(GPa) 

ν σy

(MPa) 

Et

(MPa) 

c0

(m/s) 

Inconela 8.40 201.33 0.290 — — 4895.70 

Steel 7.85 206.91 0.300 830.00 0.0 5134.00 

Aluminum 2.70 68.95 0.285 249.00 840.00 5053.42 

Ceramic 3.95 370.00 0.220 — — 9678.37 

a

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

In the SHPB experiment, the most common measured quantities are the impact velocity of the 

projectile, axial strain on the bar surface as a function of time via surface mounted SGs, and the 

axial and transverse strains on the specimen surface as a function of time. In the numerical 

experiment, displacement and velocity of nodes, strain and stress of the elements, interface 

forces, and material and global energies can be investigated as a function of time. Time history 

data of selected nodes, elements, and interfaces of interest are stored during solution and 

analyzed during the postprocessing phase. The validated model, as described in reference (13), 

is then used for detailed numerical analyses. 

In order to enforce a known boundary condition, a parametric stress pulse is taken as the input to 

the impact face of the IB with four parameters: At , Bt , Ct , and P (figure 6). By suitable max

choice of these parameters: different pulse shapes can be obtained (e.g., rectangular, trapezoidal, 

and triangular). Detail parameters used in a numerical experiment will be described in each 

different case study.
9 

Figure 6. Loading history on the impact face of the IB. 

3. Effect of Nonplanar Bar-Specimen Interface: The Problem 

It is well known that the particle velocity of the free end of a long bar is twice the particle 

velocity of the propagating pulse, and that of a built-in end is zero. Figure 7 shows the schematic 

of a cylindrical specimen sandwiched between IB and TB. Clearly, if the specimen diameter is 

smaller than that of the bars, and the acoustic impedance of the specimen is comparable with that 

of the bars, then the particle velocity of the free surface (R rR S B < < ) will be higher than that of 

the interface where the bar and the specimen is in contact ( S 0rR < < ). In this case, the radial 

distribution of axial deformation, j

i u (r) , of the IB-S and S-TB interfaces is not uniform, i.e., the 

bar-specimen interfaces undergo a nonplanar deformation (12, 13). 

It has been shown (13) that this nonplanar deformation of the IB-S interface produces an average 

displacement of the specimen at this interface, which is smaller than the average displacement of 

the IB edge at the IB-S interface. Similar argument can be made for the S-TB interface 

deformation also. Thus, the average strain of the specimen measured from the reflected pulse is 

always higher than the actual strain in the specimen (13). Because the deformation of the 

bar-specimen interfaces is nonplanar, in the elastic phase of deformation, the nonuniform radial 

displacement field on the specimen in the bar-specimen interfaces produces a nonuniform 

distribution of axial stress along the length of the specimen, which can be measured by 

measuring the axial stress along the length on the surface of the specimen (13). This nonplanar 

interface deformation can cause barreling of the specimen. Thus, in the elastic deformation 

phase of a smaller diameter hard specimen (e.g., composites in the fiber directions, and ceramics 

as compared to metallic bars), two important assumptions of 1-D Hopkinson bar analysis 

(i.e., [a] bar-specimen interfaces remain planar and [b] specimen is under uni-axial stress state) 

fail to hold true. However, in the plastic phase of deformation, the specimen is found to achieve 

uni-axial stress state along the length, which is the outcome of radial outward plastic flow of 

materials under axial compression.

0 tB t tA C Time, t, μs

Pressure, P

Pressure BC on the 

Impact Face of IB

Pmax

0 tB t tA C Time, t, μs

Pressure, P

Pressure BC on the 

Impact Face of IB

Pmax
10 

Figure 7. Nonplanar bar-specimen interface deformation model of a small diameter 

hard specimen: j

i u – axial displacements in Z-direction; subscripts i = C,

D, and E represent bar-center, specimen-edge, and bar-edge, respectively; 

superscripts j = 1 and 2; “1” = IB-S interface; “2” = S-TB interface.*

The nonplanar deformation of bar-specimen interface is related with the nonuniform axial stress 

distribution in the specimen. To correct this problem, one can design a new experiment such that 

the bar-specimen interface remains plane at all time during dynamic deformation of the 

specimen, or can design a specimen such that the axial stress distribution in the specimen is 

uniform. In the following sections, new specimen and experiment design is presented, which 

improves the uni-axial stress distribution in the specimen and provides better planar 

bar-specimen interface conditions. 

4. Uni-Axial Stress Along the Specimen Through Specimen Design: Partial 

Solution 

The nonplanar deformation of the bar-specimen interfaces is identified as the main reason for 

nonuniform axial stress distribution along the length of the specimens. A numerical simulation 

with a cylindrical ceramic specimen of specimen diameter to bar diameter ratio, DS /DB = 0.60, 

and specimen length to specimen diameter ratio, HS /DS = 1.00, which is equivalent to the 

dimensionless specimen length, ( ) ( ) ( ) 2

S SB SS S BS D D D H D D D H 0.60, ˆ = = ⋅= has been

 *

Adapted from references (12) and (13). 

r, X, Y

Z

DB

DS

HS

uE

1

uD

1

uC

1

RB

RS

uE

2

uD

2

uC

2

0

1

2

IB TB

SP

r, X, Y

Z

DB

DS

HS

uE

1

uD

1

uC

1

RB

RS

uE

2

uD

2

uC

2

0

1

2

IB TB

SP
11 

performed with a triangular input stress pulse ( At 99 = μs, Bt 101 = μs, Ct = 200 μs, and 

Pmax = 500 MPa); parameters are described in figure 6 of duration T = 200 μs. Detailed results 

of this simulation are presented in reference (13). The IB and TB ( D 25.4 B = mm) considered in 

this simulation were made from steel (see table 2 for properties). The cross section of the bar is 

modeled with 195 elements, and the specimen cross-section has one-to-one node connectivity for 

stable contact modeling. The incident, reflected and transmitted stress in the bars, is presented in 

figure 8a as dotted lines with open symbols. It is clear from figure 8a that the specimen is loaded 

under compression during the first half of the incident pulse ( 0 t / T 0.50 < < ), and the second 

half of the pulse represents unloading ( 0.50 t / T 1.00 < < ). Figure 9a shows the contours of 

stress distribution in the specimen at three different times ( t / T 0.15, 0.30, 0.45 = ) during the 

ramp-loading phase. The stress amplitude is highest at time, t / T 0.45 = , and the stress 

concentration is visible at the edges of the specimen. A similar profile is also obtained by 

Anderson et al. (38) while modeling the compression of cylindrical specimen with truncated 

cones as loading block in the SHPB setting. Figure 9 also shows that the stress on the free 

surfaces (R rR S B < < ) of the bar-specimen interfaces is zero. 

Figure 8. Numerical Hopkinson bar responses for two different test cases. 

4.1 Specimen Design 1: Cylindrical Specimen With Chamfered Edges 

The nonplanar deformation model presented in figure 7 suggests that a specimen with curved 

loading faces can eliminate the nonuniform axial stress distribution in the specimen. While the 

shape of the curve to which the specimen loading surfaces should be machined can be 

determined by solving the nonlinear contact problem, it is obvious that this solution process is 

extensive in nature. To demonstrate the concept, a cylindrical specimen with chamfered edges is 

considered instead (figure 8b). The finite element model of this chamfered specimen is 

presented in figure 10. The geometry of the chamfer can be described by two variables, LR and 

LH, as shown in figure 8b. 

(a) Bar Responses 

-600

-450

-300

-150

0

150

0 100 200 300 400 500 600 700

Reflected

Pulses

Incident

Pulses

Transmitted

Pulses

SolidLineswith

SolidSymbols:

CylindricalSpecimen

withChamferedEdges

DottedLineswithOpenSymbols:

CylindricalSpecimen

Time, t, μs.

Stress in the Bar, σZ, MPa.

LR

LH

Z

r, X, Y

LR

LH

Z

r, X, Y

LR - Dimension along radius, 

LH - Dimension along length 

(b) Notations – Chamfered 

Specimen; 
12 

t/T = 0.15 t/T = 0.30 t/T = 0.45 t/T = 0.15 t/T = 0.30 t/T = 0.45

(a) Cylindrical Specimen (b) Specimen With Chamfered Edge 

Fringe Levels: Axial Compressive Stress, σZ , MPa 

1: 0 ~ 100 

2: 100 ~ 300 

3: 300 ~ 500 

4: 500 ~ 700 

5: 700 ~ 900 

6: 900 ~ 1100 

7: 1100 ~ 1300 

8: 1300 ~ 1500 

9: 1500 ~ 1700 

10: 1700 ~ 1900 

11: 1900 ~ 2100 

12: 2100 ~ 2300 

Figure 9. Contours of axial stress distribution in the specimen at a different time. 

The numerical model of the chamfered specimen is loaded with the same boundary condition as 

in the case of a pure cylindrical specimen. The reflected and transmitted stresses in the bars 

(figure 8a, solid lines with solid symbols) appear to be a little different than the case of a 

cylindrical specimen. The contour of axial stresses at different times in the case of the specimen 

with chamfered edges (figure 9b) appears to be more uniform than the cylindrical specimen. It 

has been shown in reference (13) that the uniformity of the distribution of the axial stress in the 

specimen along the length can be represented by plotting the axial stresses on the surface of the 

specimen along the length as a function of time (figure 11a). In the elastic phase of deformation, 

the axial stress distribution on the surface of cylindrical specimen is found to be nonuniform at 

all time. The axial stress near the bar-specimen contact interfaces is higher than the midlength of 

the specimen, and the distribution has an elliptical shape. The distribution of axial stresses on 

the surface of a cylindrical specimen with chamfered edges is shown in figure 11b. As expected, 

the stress distribution on the surface of the specimen is almost uniform along the length of the 

specimen, except at the chamfered edges. At the chamfered edges, there are additional free 
13 

(a) FE Model of IB (Bottom), SP 

(Middle), and TB (Top) 

(b) Cylindrical Specimen With Chamfered 

Edge, L 0.35 R = mm, L 0.05 H = mm. 

Figure 10. Quartersymmetric finite element model of Hopkinson bars and cylindrical ceramic specimen with 

chamfered edges, D / D = 0.60 S B , H / D 1.00 S S = , S D = 0.60. ˆ

 (a) Cylindrical Specimen, Reproduced from (b) Cylindrical Specimen With Chamfered 

 reference (13), figure 25b. Edges 

Figure 11. Axial stress distribution on the surface of ceramic specimen at a different time, ˆt t/T = , S D 0.60 ˆ = , 

r / R 1.00 = , Max σ= = Z-IB max P 500 MPa. 

surfaces, on which normal stress components are zero. This study shows that by simply making 

chamfered edges on both sides of the specimen, it is possible to obtain uniform axial stress 

condition in the elastic deformation phase. 

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1.0

t/T = 0.05

t/T = 0.10

t/T = 0.15

t/T = 0.20

t/T = 0.25

t/T = 0.30

t/T = 0.35

t/T = 0.40

t/T = 0.45

Z/H.

σZ

/σMax Z-IB

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

t/T = 0.0

t/T = 0.05

t/T = 0.50

t/T = 0.05, 0.10, 0.15, ...., 0.50

Z/H.

σZ

/σMax Z-IB.
14 

In reference (13), it has been shown that the nonuniform distribution of axial stress on the 

surface of cylindrical specimen has self-similar behavior under ramp loading in the elastic phase 

of deformation, which can be shown by normalizing the axial stress by that at the midlength of 

the specimen (figure 12). In figure 12, the self-similar behavior of axial stress on the surface of a 

cylindrical specimen with chamfered edges is also presented. This figure shows the benefit of a 

chamfered specimen in attaining the uniform stress distribution in most part of a cylindrical 

specimen. 

Figure 12. Distribution of dimensionless axial stress along the length of a cylindrical 

specimen with and without chamfered edges. 

The axial stress distribution along the radial direction of the specimen at different Z / H locations 

of a cylindrical specimen at time ˆt = t / T = 0.25 is presented in figure 13. In figure 13a, the 

axial stress is normalized with the maximum axial stress in the incident pulse. 

The axial stress distribution in the radial direction is almost uniform in the range, 

0.10 < Z / H < 0.90, which is also evident from figure 12. In figure 13b, the axial stress is 

normalized with the axial stress at location r / R = 0.025 and plotted as a map along the length of 

the specimen. This figure clearly shows that the axial stress distribution is uniform over the 

specimen length except for a small region around the chamfered edged. It has been shown in 

reference (13) that the uniform distribution of axial stress on the surface of a cylindrical 

specimen along the length guarantees the overall uniformity of axial stress in the specimen 

(in the plastic deformation phase). Figure 13 proves the validity of that general statement in the 

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

t/T = 0.05, 0.10, 0.15, ...., 0.50

Cylindrical

Specimen

with

Chamfered

Edges

Cylindrical

Specimen

Z/H.

σZ

/σZ/H = 0.50

Z .
15 

Figure 13. Distribution of axial stress in the radial direction at different Z / H locations of a cylindrical specimen 

with chamfered edges, ˆt t / T 0.25. = =

elastic deformation phase in case of a cylindrical specimen with chamfered edges. Chamfering 

the edges of the specimen can thus effectively minimize the problem of nonuniform axial 

stress distribution of a small diameter cylindrical specimen. The analysis of the 

dog bone/dumbbell-shaped specimen design suggested by Deltort et al. (34) is presented next. 

4.2 Specimen Design 2: Dog Bone/Dumbbell-Shaped Cylindrical Specimen 

One can analyze the distribution of axial stress on the surface of a cylindrical specimen in the 

elastic deformation phase (figure 12) and can heuristically make a hypothesis that a traditional 

dog bone/dumbbell shape cylindrical specimen can also provide uniform axial stress distribution 

on the surface of the specimen in the gage section. It is also obvious that a specimen with a 

diameter equal to the bar minimizes the nonplanar deformation of the bar-specimen interfaces 

(12, 13). The cylindrical dog bone/dumbbell-shaped specimen proposed by Deltort et al. (34) 

also considered the end of the specimen to be of equal diameter to the bars. This specimen and 

associated parameters to define the specimen geometry are presented in figure 14. Two 

important parameters of the dog bone specimen are the length of the right circular cylinder part 

at the specimen ends, LF, (which will be in contact with the bars), and the length of the parabolic 

section, LC, of the specimen. The length of the cylindrical gage section is denoted by usual 

nomenclature, HS. 

To be consistent with our analyses of cylindrical specimens with and without chamfered edges, 

the specimen dimensionless parameters are kept unchanged (i.e., DS / DB = 0.60, HS / DS = 1.00, 

S D 0.60 ˆ = ). Because the specimen aspect ratio is taken as HS / DS = 1.00, the total length of the 

dog bone-shaped specimen is longer than the cylindrical specimens. 

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Z/H = 0.01

Z/H = 0.06

Z/H = 0.11

Z/H = 0.24

Z/H = 0.49

Z/H = 0.74

Z/H = 0.99

r/R.

σZ

/σMax Z-IB.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

2

1

0

2

1

r/R.

Z/H.

t/T = 0.25

r/ R=0.025

Z

Z

σ

σ

r/ R=0.025

Z

Z

σ

σ 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

2

1

0

2

1

r/R.

Z/H.

t/T = 0.25

r/ R=0.025

Z

Z

σ

σ

r/ R=0.025

Z

Z

σ

σ

(a) Axial Stress Normalized with Max σZ-IB (b) Axial Stress Normalized with r / R 0.025

Z

= σ
16 

Figure 14. The parametric definition of a cylindrical 

dog bone/dumbbell-shaped specimen 

proposed by Deltort et al. (34). 

A finite element model of the dog bone-shaped specimen is developed by keeping the same 

strategy of one-to-one correspondence of nodes between the contact interfaces and is presented 

in figure 15a. Both the bar and specimen cross-section is modeled using 144 elements. The 

specimen parameters have been marked on the FE model, and the different sections and 

interfaces are highlighted. Similar loads and boundary conditions are used as in the case of 

specimen design 1. Figure 15b shows the contour of axial stress distribution in the dog 

bone-shaped specimen at three different times, as is also presented in previous cases (figure 9). 

The range of fringes is also the same for comparison with figure 9. The axial stress distribution 

of the dog bone-shaped specimen is superior to that of the cylindrical specimen with chamfered 

edges. The distribution of axial stress on the surface of the dog bone-shaped specimen along the 

length is presented in figure 16, where the Z-coordinate at the beginning of the gage section is 

taken as zero to make a comparison with the cylindrical specimens. The results for cylindrical 

specimens with and without chamfer are also plotted for comparison. There still remains some 

nonhomogenous distribution of axial stress at the beginning of the gage section; however, the 

overall distribution is superior to that of the cylindrical specimen with the chamfered edge. 

A dog bone-shaped shaped cylindrical specimen can provide a uni-axial stress condition in the 

specimen in the elastic deformation phase; however, the calculation of the specimen average 

strain from bar responses becomes problematic due to the presence of the additional length of the 

specimen in addition to the gage section. However, because the specimen has uni-axial stress 

state over the gage length, SGs can be mounted on the surface of the specimen to measure the 

specimen strain, which is also true for the case of the cylindrical specimen with chamfered 

edges. It is interesting to note that, in testing of ceramic materials, SGs are used on the specimen 

to measure the specimen strain along with shaped pulses (27). However, uncertainty remains in 

selecting an SG of specific gage length for a specific specimen length, even if one decides to 

bond the SG in the midlength of the specimen. From the present analysis, a major conclusion 

HS LC LF

DS DB

r, X, Y

Z

HS LC LF

DS DB

r, X, Y

Z
17 

IB

TB

LF

LC

HS

IB

TB

LF

LC

HS

7.62mm

8.28mm

7.77mm

9.34mm

12.7mm

LC = 7.62mm

LF = 6.35mm

7.62mm

8.28mm

7.77mm

9.34mm

12.7mm

LC = 7.62mm

LF = 6.35mm

t/T = 0.15 t/T = 0.30 t/T = 0.45

(a) FE Model of the Dog Bone 

Specimen 

(b) Axial Stress Distribution 

Fringe Levels: Axial Compressive Stress, σZ , MPa 

1: 0 ~ 100 

2: 100 ~ 300 

3: 300 ~ 500 

4: 500 ~ 700 

5: 700 ~ 900 

6: 900 ~ 1100 

7: 1100 ~ 1300 

8: 1300 ~ 1500 

9: 1500 ~ 1700 

10: 1700 ~ 1900 

11: 1900 ~ 2100 

12: 2100 ~ 2300 

Figure 15. Contours of axial stress distribution in the dog bone-shaped specimen at a different time. 

can be made that Hopkinson Bar testing of linear-elastic materials (e.g., composites in fiber 

direction and ceramics) can be performed while satisfying the uni-axial stress condition in the 

elastic phase of deformation if a chamfered or dog bone-shaped specimen is used. The other 

conclusion is that one can use SG to measure specimen strain with confidence, knowing the 

fact that the specimen is under uni-axial stress state in case of a chamfered and a dog 

bone/dumbbell-shaped specimen. 

Both of the specimen designs have their own limitations. The chamfered cylindrical specimen 

does not guarantee the planar bar interface condition, and thus the solution is not complete. The 

dog bone-shaped specimen having equal diameter guarantees planar bar-specimen condition, 

however, requires an additional SG to measure the strain in the specimen. It is also important 

that the specimen remains under stress equilibrium. The deviation of stress equilibrium in the 

specimen is usually characterized by the factor R / 2 F F /F F = ∆σ σ = ⋅ − + avg 1 2 1 2 ( )( ) (12, 13) and 

is presented in figure 17 for all three cases. The forces, F and 1 F , at the IB-S and S-TB 2

interfaces, are taken from the time history of contact forces at the corresponding interfaces. 
18 

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Dog BoneShaped

Cylindrical

Specimen

t/T = 0.10, 0.15, ...., 0.45

Cylindrical

Specimen

with

Chamfered

Edges

Cylindrical

Specimen

Z/H.

σ

/ Z

σZ/ Z

H

=

0.

5

0.

Figure 16. Distribution of dimensionless axial stress along the length of a dog 

bone-shaped specimen and that for cylindrical specimens with and without 

chamfered edges. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Dog Bone Cyl. Specimen

Chamfered Cyl. Specimen

Cylindrical Specimen

t/T.

R

=

∆

/σ

σa

v

g =

(

2

F

- 1

F

) 2 /

(

F1 +

F

) 2 .

Figure 17. Deviation from stress equilibrium of different specimen designs.
19 

It has been shown by the authors (13) that the specimen is not under stress equilibrium at 

anytime as can also be seen from figure 17. It is interesting that the cylindrical specimen with 

chamfered edges does not provide any better stress equilibrium for the specimen. However, the 

dog bone/dumbbell shaped specimen, being longer in length, has the deviation from equilibrium, 

which is much higher than the cylindrical specimens with chamfered edges. In both the cases, 

additional considerations should be undertaken to improve the stress equilibrium in the 

specimen. In separate works (39, 40), analytical techniques have been proposed to address the 

issues related to deviation of stress equilibrium. However, in general, better stress equilibrium 

can be achieved by using thinner specimens (12). 

5. Planar Bar-Specimen Interface Condition Through Experiment Design: 

Complete Solution 

The nonplanar deformation model of a small diameter hard specimen is presented in figure 7 and 

is also discussed in references (12, 13, 34). The main reason for the nonplanar deformation of 

the bar-specimen interface is that the free end of the IB, which is not in contact with the 

specimen (RS < r < RB), moves with higher particle velocity than the portion in contact with the 

specimen (0 < r < RS), as described in figure 7. If one uses a specimen with diameter equal to 

the bar (DS = DB), the bar-specimen interfaces will remain planar. However, if high strain rate 

stress-strain diagram up to the failure of the specimen is sought, a realistic engineering practice is 

to use a small diameter specimen such that the stress level in the specimen is sufficiently high to 

cause damage or failure. If a smaller diameter specimen is used, ideally one can use a hollow 

cylindrical tube to load the free end of the specimen. In that case, the transmitter bar diameter 

should be equal to the specimen diameter to support the specimen on the transmission end. A 

new compression SHPB experimental technique is proposed in this report for the first time to 

guarantee the planar bar-specimen interface condition, and is presented in figure 18. 

5.1 Compression SHPB With a TT 

The new compression SHPB has several unique features, which include a transmitter 

/transmission bar (TB) that is equal to the SP diameter, or a little greater diameter than the 

specimen to accommodate the radial expansion due to Poisson’s effect. It has a TT with an inner 

diameter a little greater than the TB, such that the TB can have a sliding fit inside the TT; and the 

outer diameter of the TT is equal to the diameter of the IB. The length of the TT should be more 

than 4× the SB length, and should be approximately half the length of the TB. Independent SGs 

should be mounted on the IB, TT, and TB. Figure 18 shows that both the specimen and the TT 

are in contact with the IB. When the incident pulse reaches the IB-S/IB-TT interface, a part of it 

is transmitted to the TT and a part to the specimen. If the TT and the IB are made from the same 

material, the reflection coefficient of the area of IB that is in contact with the TT is zero (acoustic 

impedance of the IB and TT tube being the same, i.e., Z c cZ IB IB 0IB TT 0TT TT = ρ =ρ = ).
20 

(a) Schematic Diagram 

(b) Notations 

Figure 18. A new compression SHPB experimental set-up with TT. 

The reflection coefficient of the part of IB that is in contact with the specimen depends on the 

impedance of the specimen. If the impedance of the specimen is 50% of the bar, then the 

reflection coefficient of the IB-S contact area is 1 − 3 (negative one-third), and if it is 50% more 

than the bar, then the reflection coefficient is 1 + 5 (positive one-fifth). Because the reflection 

from the IB-TT interface is zero, the reflected pulse recorded by the SG mounted on the IB 

surface will consist only of the reflections from the IB-S contact interface and from the free 

surface of the IB if there is any clearance between the specimen and the TT. Thus, the particle 

velocities at IB-S and IB-TT interfaces can be expressed as 

IB-S IB IB

1 0IB I R u = –c ×⎡ε (t) (t) – ε ⎤ ⎣ ⎦  (6) 

and 

IB-TT IB TT

1 0IB 0TT I T u = –c ×  ε (t) (t) = –c ×ε , (7) 

and the corresponding displacements as 

t

IB-S IB IB

1 0IB I R u c dt ⎡ (t) (t)⎤ ⎣ ⎦ = − ⋅ ε −ε ⋅ ∫ (8) 

and

SB IB TT TB SP

SG SG

SG

IB TT

TB

SP

IB TT

u −

1

IB S

u −

1

 IB TB

u −

2

1 2

( )t IB

I ε

( )t IB

R ε

( )t TT

T ε

( )t TB

T ε

IB TT

TB

SP

IB TT

u −

1

IB S

u −

1

 IB TB

u −

2

1 2

( )t IB

I ε

( )t IB

R ε

( )t TT

T ε

( )t TB

T ε
21 

t t

IB-TT IB TT

1 0IB 0TT I T u c dt c dt =− ⋅ ε ⋅ =− ⋅ ε ⋅ (t) (t) ∫ ∫ , (9) 

where subscript 1 represents the IB-S/IB-TT interface, and the superscripts denote the location 

where the properties are measured at. If the IB-S/IB-TT interface remains planar then the 

following equity should exist: 

IB-S IB-TT u =u 1 1 . (10) 

If this equity exists, then either of equations 8 or 9 can be taken as the displacement of the 

IB-S/IB-TT interface, otherwise one can take an algebraic average as the displacement at this 

interface: 

( ) IB-S/ IB-TT IB-TT IB-S u u u2 1 11 = + . (11) 

A complex stress wave reverberation in the specimen takes place, and the stress wave is 

transmitted to the TB. The particle velocity and displacement at the S-TB interface can then be 

expressed as 

S-TB TB

2 0TB T u c  = − ⋅ε (t) (12) 

and 

t

S-TB TB

2 0TB T u c dt = − ⋅ε ⋅ (t) ∫ , (13) 

where subscript 2 represents the S-TB interface. 

It is well known that the stress wave propagation in finite diameter bars is dispersive (3, 41), and 

thus a dispersion correction of the strain signals recorded on IB, TT, and TB should be 

performed (10, 12). It is important to mention that the dispersion correction methodology 

automatically performs the time sifting of incident, reflected and transmitted pulses to a common 

zero, and makes the algebraic manipulation easy. Once the dispersion correction procedure is 

performed, the average strain of the specimen can be expressed as 

( ) S-TB IB-S/ IB-TT

S 21 S ε= − (t) uu H . (14) 

Because the free end of the IB-S interface is loaded with the TT and the TB diameter is equal to 

the specimen diameter, it is anticipated that the bar-specimen interfaces will remain planar at all 

time. Thus the major problem of nonplanar bar-specimen interface condition of a smaller 

diameter hard specimen can be resolved by the new compression SHPB with TT. 

Following the 1-D stress wave propagation assumptions (12), the forces in the IB-S/IB-TT 

interface and S-TB interface can be expressed as 

IB IB TT F (t) A E (t) (t) A E (t) 1 IB IB I R TT TT T = ε +ε − ε ⎡ ⎤ ⎣ ⎦ , (15)
22 

and 

TB F (t) A E (t) 2 TB TB T = ε . (16) 

The average stress in the specimen then can be expressed as 

σ= + ⋅ S 12 S (t) F (t) F (t) 2 A [ ] , (17) 

which is equivalent to the “3-wave” analysis as described by Gray (24). Because equation (17) 

use four different measured strains to calculate the average specimen stress, this analysis can be 

termed as “4-wave” analysis. 

The use of a TT is reported in literature by Harding and Huddart (21) in the dynamic punch shear 

testing technique, and by Nemat-Nasser et al. (8) in the tri-axial Hopkinson bar test technique. 

However, the unique use of TT to guarantee the planar bar-specimen interface condition is 

reported in this report for the first time. The numerical experiment of this new SHPB design is 

presented next to provide the proof of concept and validity of analysis. 

5.2 Numerical Simulation of Compression SHPB With TT 

The cross section of the specimen and the TB is modeled with 280 and 300 elements, 

respectively; while the IB and TT cross sections are modeled with 540 and 240 elements, 

respectively. Along the length of the IB and TB, 400 elements are used as described for the 

earlier case; however, 200 elements along the length of TT are used. A specimen with 

chamfered edges is used in this model, which guarantees the uni-axial stress along the length of 

the specimen. The parameters of the chamfered specimen are the same as described earlier. 

Figure 19 shows the FE model at the bar-specimen interfaces location. Properties of steel are 

used to model the bars, and the specimen is modeled with elastic-plastic aluminum and elastic 

ceramic materials. 

IB SP

TT

TT

TB

Figure 19. Finite element model of the compression SHPB with TT.
23 

The geometric dimensions of the SHPB with TT model are as follows: LIB = 1524 mm, 

DIB = 25.4 mm, LTT = 562 mm, ID DTT = 15.875 mm, OD DTT = 25.4 mm, LTB = 1524 mm, 

DTB = 15.1 mm, HS = 15.24 mm, and DS = 15.1 mm. These dimensions for the bars and the 

specimen represent a realistic experiment, where the specimen diameter is a little less than the 

TB, and the diameter of the TB is also a little less than the inner diameter of the TT. A triangular 

input stress pulse ( At 99 = μs, Bt 101 = μs, Ct 200 = μs, and P 500 max = MPa) of duration 

T 200 = μs is used at the impact end of the projectile. The bar responses (element stresses on the 

bar surface at midlength) are presented in figure 20 with aluminum and ceramic specimens for 

the IB, TB, and TT. Note that the reflected and transmitted pulses measured at midlength of the 

IB and TB have the same time references; however, the transmitted pulse measured at midlength 

of the TT appears early in time because the length of TT is half of the IB. In the case of the 

aluminum specimen, a reflected pulse with a nearly constant amplitude up to 500 μs represents 

the elastic deformation phase, and the increase in amplitude after that represents the plastic 

deformation, which is also evident from the transmitted pulse. However, for the ceramic 

specimen, the reflected pulse has near zero amplitude because the impedance ratio of steel and 

ceramic is 1.054. As described earlier, the stress pulse in the TT has the same order of 

magnitude as the incident pulse and can be used to measure the displacement of the IB-S/IB-TT 

interface of the specimen. 

The stresses in the bars are dispersion corrected (12), and then the time-shifted stresses are 

converted to strains in the bars. Equations 6–17 are used in calculating the average strain and 

stress in the specimen. Before presenting the stress-strain data, one needs to prove that the 

bar-specimen interface is planar and the specimen is under uni-axial stress. In addition, one also 

needs to comment on the stress equilibrium. If these three basic assumptions made in 1-D 

Hopkinson bar analysis hold true, then the experiment is considered as a valid experiment. 

Three dimensionless nonplanar interface parameters, i u – i = IB, TT, TB, can be defined to ˆ

express the deviation from the planar interface condition for the bar-specimen interfaces. 

( ) CAA

IB Z Z Z u uuu ˆ (t) = − , (18) 

( ) CBB

TT Z Z Z u uuu ˆ (t) = − , (19) 

and 

( ) EDD

TB Z Z Z u uuu ˆ (t) = − , (20) 

where, the displacement components, j

Z u , are outlined in figure 21, and j = A, B, C, D, E.
24 

Figure 20. Bar responses of the new compression SHPB with TT. 

Figure 21. Notations for axial displacements measured at different radial 

locations of different bars. 

Figures 22 and 23 show the time history of the dimensionless nonplanar interface parameters for 

ceramic and aluminum specimens, respectively. In these figures, the nonplanar interface 

parameters IB u , ˆ TT u , and ˆ TB u (given by equations 18–20) for the new compression SHPB with ˆ

TT are presented and denoted by IB-S/IB-TT interface, IB-TT interface, and S-TB interface, 

respectively. In addition, the nonplanar interface parameters at IB-S interface and S-TB 

interface for classic SHPB with cylindrical specimens are also presented. The nonplanar 

interface parameters have maximum value at small displacements, which correspond to small 

time (ˆt 0 ≈ ) and exponentially decrease to plateau level at large displacements, and can be 

expressed as 

( ) ˆt

i i0 ut u e ˆ ˆ ˆ −β⋅ = +α⋅ , (21) 

-600

-400

-200

0

200

400

600

0 100 200 300 400 500 600 700

Transmission

Tube Response

Transmitted

Pulse

Reflected

Pulse

Incident

Pulse

Time, t, μs.

Stress in the Bars, σ, ΜΠα.

-600

-400

-200

0

200

400

600

0 100 200 300 400 500 600 700

Transmission

Tube Response

Transmitted

Pulse

Reflected

Pulse

Incident

Pulse

Time, t, μs.

Stress in the Bars, σ, MPa.

(a) With Aluminum Specimen (b) With Ceramic Specimen 

IB

TT

TB

SP

A

Z u

C

Z u

B

Z u

D

uZ

E

Z u

IB

TT

TB

SP

A

Z u

C

Z u

B

Z u

D

uZ

E

Z u
25 

(a) Comparison With Classic Technique 

where, i0 u , ˆ α, and β are fitting constants. The fitting constant, i0 u represents the plateau value ˆ

and the addition of constants, i0 uˆ + α represent the maximum value at ˆt 0 = . In the case of 

classic compression SHPB with cylindrical ceramic specimen (figure 21a), the parameter IB u is ˆ

found to be positive with a maximum value of 0.463, which exponentially decays to a plateau 

value of 0.071, and the parameter TB u is found to be negative with a maximum value of ˆ −0.698, 

which exponentially decays to a plateau value of −0.072 (table 3). This study proves that, in fact 

the bar-specimen interfaces, as described in figure 7, are nonplanar, and the curvature of the 

S-TB bar interface has an opposite sign to that of the IB-S interface. 

Figure 22. Nonplanar interface parameter, i uˆ , as a function of time, ceramic specimen. 

Figure 23. Nonplanar interface parameter, i uˆ , as a function of time, aluminum specimen. 

i uˆ

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

S-TB Interface

IB-TT Interface

IB-S/IB-TT Interface

Bar-Specimen Interfaces

New Compression

SHPB with TT

S-TB Interface

Classic Compression SHPB

IB-S Interface

Classic Compression SHPB

t/T.

i uˆ

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

S-TB Interface

IB-TT Interface

IB-S/IB-TT Interface

Bar-Specimen Interfaces

New Compression

SHPB with TT

S-TB Interface

Classic Compression SHPB

IB-S Interface

Classic Compression SHPB

t/T.

ui ˆ

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

S-TB Interface

IB-TT Interface

IB-S/IB-TT Interface

Average of IB-S/IB-TT 

and IB-TT Interfaces

Average of

IB-S/IB-TT and

IB-TT Interfaces

IB-TT Interface

S-TB Interface

IB-S/IB-TT Interface

t/T.

ui ˆ

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

S-TB Interface

IB-TT Interface

IB-S/IB-TT Interface

Average of IB-S/IB-TT 

and IB-TT Interfaces

Average of

IB-S/IB-TT and

IB-TT Interfaces

IB-TT Interface

S-TB Interface

IB-S/IB-TT Interface

t/T.

(a) Comparison With Classic Technique (b) Extended View for New Technique

uiˆ

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

S-TB Interface

IB-TT Interface

IB-S/IB-TT Interface

Bar-Specimen Interfaces

New Compression

SHPB with TT

S-TB Interface

Classic Compression SHPB

IB-S Interface

Classic Compression SHPB

t/T.

uiˆ

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

S-TB Interface

IB-TT Interface

IB-S/IB-TT Interface

Bar-Specimen Interfaces

New Compression

SHPB with TT

S-TB Interface

Classic Compression SHPB

IB-S Interface

Classic Compression SHPB

t/T.

i uˆ

-0.20

-0.18

-0.16

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.10

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

S-TB Interface

IB-TT Interface

IB-S/IB-TT Interface

t/T.

i uˆ

-0.20

-0.18

-0.16

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.10

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

S-TB Interface

IB-TT Interface

IB-S/IB-TT Interface

t/T.

(a) Comparison With Classic Technique (b) Extended View for New 
26 

Table 3. Nonplanar bar-specimen interface parameters and fitting constants for 

ceramic specimen and steel bars. 

Ceramic Specimens 

Parameters Classic SHPB 

New SHPB 

With TT 

IB uˆ TB uˆ IB uˆ TB uˆ

i0 uˆ 0.0709 −0.0716 0.0031 −0.0034 

α 0.3920 −0.6260 0.0209 −0.0354 

β 7.34 7.57 26.4 8.22 

In the case of the new compression SHPB with TT and with ceramic specimen, the calculated 

values of the nonplanar interface parameters are an order of magnitude lower than the classic 

case; however, these are not absolutely zero. A little free surface on the IB-S/IB-TT interface 

and the specimen with different acoustic impedance than the bars are the main reasons for the 

finite but relatively smaller values of the nonplanar interface parameters. Figure 21b shows a 

close-up view of these parameters. Table 3 shows the fitting parameters of the nonplanar 

interface parameters for IB-S and S-TB interfaces. The plateau value at IB-S/IB-TT is found to 

be (ûIB0 = 0.0031), which is only 4.4% as compared to the classic case (ûIB0 = 0.0709). The 

maximum value in this case is found to be (ûIB0 + a = 0.024), which is ~5.2% of the classic value 

(ûIB0 + a = 0.463). Similar reduction is observed in the S-TB interface. This study validates the 

hypothesis made prior to the numerical experiment that the new compression SHPB with TT will 

guarantee a planar-bar-specimen interface condition for small-diameter-hard specimens in the 

elastic phase of deformation. In a realistic experimental setup, the specimen diameter should be 

a little less than the transmission bar, and there would be a little free surface on the IB-S/IB-TT 

interface, and thus the bar-specimen interfaces, will not be perfectly nonplanar. In the case of 

ceramic specimens and steel bars, the classic method provides 46%–70% error in small strain 

measurement and ~7% error for large strain measurements. However, this new technique with 

TT will provide much better accuracy than the classic method with the limit of 2%–4% error for 

very small strain measurement and 0.31%–0.34% error for relatively larger strains. 

It is interesting to note that the error in the IB-TT interface is similar (same order of magnitude) 

to that of the IB-S/IB-TT interface, but is negative instead of positive. If equation 11 is used to 

calculate the average displacement at the IB-S/IB-TT interface, the error will be minimum (near 

zero) as shown in figure 22b by the legend “Average of the IB-S/IB-TT and IB-TT Interfaces.” 

It has been shown that the error in the S-TB interface is an order of magnitude smaller in the case 

of the SHPB with TT; the use of equation 14 will provide a sufficiently accurate measurement of 

strain in the elastic deformation phase (small strain) of a ceramic (linear-elastic) specimen.

The aluminum specimen is acoustically softer than the bars, and thus the curvature of the 

IB-S/IB-TT interface, in the case of SHPB with TT, is found opposite to that of the classic 

case (figure 23b, table 4). This implies that the particle velocity at the center of the IB 
27 

Table 4. Nonplanar bar-specimen interface parameters and fitting constants for 

the aluminum specimen and steel bars. 

Aluminum Specimens 

Parameters Classic SHPB 

New SHPB 

With TT 

IB uˆ TB uˆ IB uˆ TB uˆ

i0 uˆ −0.0114 −0.0164 −0.0147 0.0050 

α 0.2280 −0.7250 −0.1570 −0.0404 

β 5.27 6.52 15.6 4.55 

(in contact with the specimen) is higher than the edge of the IB. In other wards, the curvature of 

the IB-S interface has the same shape and sign as that of the S-TB interface. In this case, the 

displacement measured at the IB-S/IB-TT interface will be smaller than the average 

displacement of the specimen, and consecutively the strain measured using equation 8 will be 

smaller than the specimen strain. This error in displacement measurement (under prediction) at 

the IB-S/IB-TT interface has the same order of magnitude as compared to the classic case 

(over prediction); however, the amplitude error is a little smaller. On the other hand, the error in 

the S-TB interface is greatly improved by the new SHPB with TT method. 

The amplitude of the stress pulse in the TT has the same order of magnitude as that of the 

incident pulse. A close examination of figure 22b and 23b reveals that the error in the IB-TT 

interface is negative and an order of magnitude smaller as compared to the classic case. Thus, 

the stress pulse of TT alone can be used to measure the displacement (equation 9) of the 

IB-S/IB-TT interface, irrespective of the type of the specimen. In this case, the IB responses 

(incident and reflected pulses) are redundant, which suggests that the length of the IB can be 

arbitrary. If the length of the IB is considered zero, then the compression SHPB with TT reduces 

to a direct impact Hopkinson pressure bar (HPB) with TT (figure 24a). One of the problems of 

direct impact HPB is that the displacement of the impact face of the specimen cannot be 

measured without a high-speed camera. If a direct impact HPB with TT is used, the 

displacement of the impact end of the specimen can be measured from the TT response 

(equation 9), and as usual, the displacement of the S-TB interface can be estimated from the TB 

response (equation 13). 

The analysis and numerical results presented can be applied to a hollow cylindrical specimen 

with some changes. Figure 24b shows the application of a hollow cylindrical specimen in 

conjunction with an SHPB with TT and with a direct impact HPB with TT. Materials with low 

Poisson’s ratio, e.g., metal foams, can be used as hollow cylindrical specimens. Additional 

cylindrical enclosures may be used to characterize materials under confinement. The new 

compression SHPB with TT (figure 18) and the new direct impact HPB with TT (figure 24a) 

guarantee the planar bar-specimen interface condition within reasonable engineering accuracy 

(<5%). In addition, the direct impact HPB with TT eliminates the age-old problem of 
28 

(a) Direct Impact HPB with TT 

 (b) Hollow Cylindrical Specimen with the new SHPB or Direct Impact HPB with TT 

Figure 24. HPB with TT: applications with direct impact and hollow cylindrical specimen. 

displacement measurement at the impact end of the specimen. Because the cylindrical specimen 

with chamfered edges provides uni-axial stress distribution along the length of the specimen 

under elastic deformation phase, the use of a cylindrical specimen with chamfered edges in 

conjunction with the new SHPB with TT satisfies the planar bar-specimen interface condition at 

all time. However, the problem of stress equilibrium in the specimen remains (figure 17). The 

accurate construction of a stress-strain diagram in the linear-elastic deformation phase should 

accurately predict the average stress in the specimen in addition to the accurate prediction of 

small strain/elastic deformation. The stress equilibrium in the specimen is usually not achieved 

(24, 27, 37) in the initial phase of elastic deformation (figure 17). It is a usual practice to use 

specimens with HS / DS ~ 1.00 in most SHPB applications; however, thinner specimens can 

provide better stress equilibrium. If thinner specimens are used, 0.01 < HS / DS < 0.10, the 

uni-axial stress condition of the specimen changes to plane-strain condition, and in this case, 

friction and radial inertia effects become important. The new SHPB with TT is designed for 

small strain measurement in the linear-elastic deformation phase, and it can be assumed that the 

SB TT TB SP

SG

SG

IB or SB TT TB

Hollow Cylindrical

Specimen
29 

friction and radial inertia effects are negligible. With this assumption, the effect of specimen 

thickness on the nonequilibrium stress parameter, R, is determined for three different ceramic 

specimens with chamfered edges, HS / DS = 1.00, 0.50, 0.25, and is presented in figure 25. 

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

HS/DS = 0.25

HS/DS = 0.50

HS/DS = 1.00

Chamfered Specimen

SHPB with TT

t/T.

R = ∆σ/σ

avg = 2(F1 - F2)/(F1 + F2).

Figure 25. Deviation from the stress equilibrium of the ceramic 

specimen with a different HS / DS ratio, SHPB with TT. 

Figure 25 shows that the decrease in the specimen HS / DS ratio decreases the nonequilibrium 

stress parameter, R; however, nonequilibrium exists (37). Thus, one can plot the time-averaged 

nonequilibrium stress and strain data to represent engineering stress-strain relationships of the 

material at high strain rate (figure 26). The numerical bar responses are corrected for dispersion 

following the methodology proposed by Lifshitz and Leber (10). In addition, the dispersion 

correction algorithm for cylindrical tubes and rods proposed by Ren et al. (41) using the M-H 

shell model (42, 43) is also used. 

The linear-elastic modulii of ceramic and aluminum used in the simulations were 370 GPa and 

69 GPa, respectively. In the case of ceramic specimen (figure 26a), the modulii obtained from 

the simulation in the cases of classic 1-wave, 3-wave, and SHPB with TT analyses are 158, 208, 

and 502 GPa, respectively, which corresponds to the ratio of theoretical modulus vs. simulated 

modulus, ETheo / ESimu 0.427, 0.562, and 1.357, respectively. The ratios ETheo / ESimu for the 

aluminum specimen (figure 26b) in the previously mentioned cases are 0.790, 0.764, and 1.635, 

respectively. Clearly, the classic 1- and 3-wave analyses predict higher strains due to the 

nonplanar interface condition and thus lower linear-elastic modulus. The new SHPB with TT 

overpredicts the modulus, which proves the validity of the assumption that the bar-specimen 

interfaces are nonplanar. The impedance mismatch between the SP and IB, and IB and TT 

(note that we used steel TT) is identified as the source of this error. If the impedance of the TT is 

matched with that of the specimen, this error might reduce significantly, and these issues will be 

addressed elsewhere.
30 

Figure 26. Stress-strain response of SHPB with TT and comparison with classic methods, HS / DS, DS / DIB = 0.60.

Zhao and Gary (44) and Zhao (45) proposed a combined analytical-numerical-experimental 

approach for the small strain measurement using the SHPB technique, which is computationally 

extensive and requires parametric evaluation of several parameters of a rate-sensitive material 

model, however, is considered the state-of-the-art solution of the problem. The new SHPB with 

TT and with the chamfered cylindrical specimen provides an experimental way of measuring 

small linear-elastic deformation, while satisfying all the major assumptions made in the 1-D 

SHPB analysis. 

6. Summary 

Extensive numerical analyses are carried out in the design of Hopkinson bar specimens and in 

new experiments that satisfy the uni-axial stress condition in the specimen and the planar 

bar-specimen conditions. It has been shown that a right cylindrical specimen with a chamfered 

specimen with a diameter smaller than the bars improves the uni-axial stress condition in the 

specimen. The new SHPB with TT and direct impact HPB with TT experimental techniques 

provide the planar bar-specimen interface condition much better than the traditional method. 

These new experimental techniques provide a way for small-strain measurement with sufficient 

engineering accuracy. The new direct impact HPB with TT solves the age-old problem of the 

displacement measurement at the impact end of the specimen. One-dimensional Hopkinson bar 

analysis is modified for the analysis of the new SHPB with TT technique. The new data analysis 

together with dispersion correction methodology is applied to reduce the numerical bar responses 

in to stress-strain diagrams. Results show that the new SHPB with TT provides better planar 

bar-specimen interface conditions, however, overpredicts the linear-elastic modulus, which can 

further be modified though the selection of impedance-matched TT. 

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

SHPB with TT: Dispersed, E = 502 GPa.

3-wave: Dispersed, E = 208 GPa.

1-wave: Dispersed, E = 158 GPa.

Engineering Strain, ε, mm/mm.

Engineering Stress, σ, MPa.

0

50

100

150

200

250

300

350

400

0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050

SHPB with TT: Dispersed, E = 112.8 GPa.

3-wave: Dispersed, E = 52.7 GPa.

1-wave: Dispersed, E = 54.5 GPa.

Engineering Strain, ε, mm/mm.

Engineering Stress, σ, MPa.

(a) Ceramic Specimen (b) Aluminum Specimen 
31 

7. References 

1. Hopkinson, B. A Method of Measuring the Pressure Produced in the Detonation of High 

Explosives or by the Impact of Bullets. Philosophical Transactions of the Royal Society of 

London, Series A, Containing Papers of a Mathematical or Physical Character 1914, 213, 

437–456. 

2. Kolsky, H. An Investigation of the Mechanical Properties of Materials at Very High Rates 

of Loading. Proc. Phys. Soc., London, II-B 1949, 62, 676–700. 

3. Davies, R. M. A Critical Study of the Hopkinson Pressure Bar. Philosophical Transactions 

of the Royal Society of London, Series A, Mathematical and Physical Sciences 1948, 240

(821), 375–457. 

4. Mechanical Testing and Evaluation, ASM Handbook, Volume 8; AMS International: 

Materials Park, OH, 2000. 

5. Meyers, M. A. Dynamic Behavior of Materials; John Wiley & Sons: New York, 1994. 

6. Daniel, I. M.; LaBedz, R. H.; Liber, T. New Methods for Testing Composites at Very High 

Strain Rates. Experimental Mechanics 1981, 21 (2), 71–77. 

7. Nemat-Nasser, S.; Issacs, J. B.; Starrett, J. E. Hopkinson Techniques for Dynamic Recovery 

Experiments. Proceedings of the Royal Society of London, Series A 1991, 453, 371–391. 

8. Nemat-Nasser, S.; Isaacs, J.; Rome J. Triaxial Hopkinson Techniques, Mechanical Testing 

and Evaluation, ASM Handbook, Volume 8; ASM International: Materials Park, OH, 2000; 

pp 516–518. 

9. Chen, W.; Zhang, B.; Forrestal, M. J. A Split Hopkinson Bar Technique for Low Impedance 

Materials. Experimental Mechanics 1999, 39, 1–5. 

10. Lifshitz, J. M.; Leber, H. Data Processing in the Split Hopkinson Pressure Bar Tests 

International Journal of Impact Engineering 1994, 15 (6), 723–733. 

11. Bussac, M. N.; Collet, P.; Gary, G.; Othman, R. An Optimization Method for Separating 

and Rebuilding One-Dimensional Dispersive Waves From Multi-Point Measurements: 

Application to Elastic or Viscoelastic Bars. Journal of the Mechanics and Physics of Solids

2002, 50, 321–349. 

12. Gama, B. A.; Lopatnikov, S. L.; Gillespie, J. W., Jr. Hopkinson Bar Experimental 

Technique: A Critical Review. Applied Mechanics Review August 2003.
32 

13. Gama, B. A.; Lopatnikov, S. L.; Gillespie, J. W., Jr. Numerical Hopkinson Bar Analysis: 

Validity of One-Dimensional Assumptions. ASC 2003 Conference, Gainesville, FL, 

20–22 October 2003. 

14. Lindholm, U. S.; Yeakley, L. M. High Strain Rate Testing: Tension and Compression. 

Experimental Mechanics 1968, 8, 1–9. 

15. Nicholas, T. Tensile Testing of Materials at High Rates of Strain. Experimental Mechanics

1980, 21, 177–185. 

16. Noble, J. P.; Goldthorpe, B. D.; Church, P.; Harding, J. The Use of the Hopkinson Bar to 

Validate Constitutive Relations at High Rates of Strain. Journal of Mechanics and Physics 

of Solids 1999, 47, 1187–1206. 

17. Rodriguez, J.; Chocron, I. S.; Martinez, M. A.; Sanchez Galvez, V. High Strain Rate 

Properties of Aramid and Polyethylene Woven Fabric Composites. Composites, Part B, 

1996, 27B, 147–154. 

18. Chocron Benloulo, I. S.; Rodriguez, J.; Martinez, M. A.; Sanchez Galvez, V. Dynamic 

Tensile Testing of Aramid and Polyethylene Fiber Composites. International Journal of 

Impact Engineering 1997, 19 (2), 135–146. 

19. Melin, L. G.; Asp, L. E. Effects of Strain Rate on Transverse Tension Properties of a 

Carbon/Epoxy Composite: Studied by Moire Photography. Composites, Part A, 1999, 30, 

305–316. 

20. Eskandari, H.; Nemes, J. A. Dynamic Testing of Composite Laminates With a Tensile Split 

Hopkinson Bar. Journal of Composite Materials 2000, 33 (4), 260–273. 

21. Harding, J.; Huddart, J. The Use of the Double-Notch Shear Test in Determining the 

Mechanical Properties of Uranium at Very High Rates of Strain. Proceedings of the 2nd 

International Conference on Mechanical Properties at High Rates of Strain; Harding, J., Ed., 

The Institute of Physics: London, 1980, vol. 47, pp 49–61. 

22. Ferguson, W. G.; Hauser, J. E.; Dorn, J. E. The Dynamic Punching of Metals, Dislocation 

Damping in Zink Single Crystals. Britt. J. Appl. Phys. 1967, 18, 411–417. 

23. Gilat, A. Torsional Kolsky Bar Testing, Mechanical Testing and Evaluation, ASM 

Handbook, Volume 8, ASM International: Materials Park, OH, 2000; pp 505–515. 

24. Gray, G. T., III. Classic Split-Hopkinson Pressure Bar Testing, Mechanical Testing and 

Evaluation, ASM Handbook, Volume 8; ASM International: Materials Park, OH, 2000; 

pp 462–476. 

25. Davies, E. D. H.; Hunter, S. C. The Dynamic Compression Testing of Solids by the Method 

of Split Hopkinson Pressure Bar (SHPB). J. Mech. Phys. Solids 1963, 11, 155–179.
33 

26. Follansbee, P. S. The Hopkinson Bar, Mechanical Testing and Evaluation, ASM Handbook, 

Volume 8; ASM International: Materials Park, OH, 1995; pp 198–203. 

27. Subhash, G.; Ravichandran, G. Split-Hopkinson Pressure Bar Testing of Ceramics, 

Mechanical Testing and Evaluation, ASM Handbook, Volume 8; ASM International: 

Materials Park, OH, 2000; pp 488–496. 

28. Malinowski, J. Z.; Klepaczko, J. R. Unified Analytic and Numerical Approach to Specimen 

Behavior in the Split Hopkinson Pressure Bar. International Journal of Mechanical Sciences

1986, 28 (6), 381–391. 

29. Gray, G. T., III. Split-Hopkinson Pressure Bar Testing of Soft Materials, Mechanical 

Testing and Evaluation, ASM Handbook, Volume 8; ASM International: Materials Park, OH, 

2000; pp 488–496. 

30. Chen, W.; Zhang, B.; Forrestal, M. J. A Split Hopkinson Bar Technique for Low Impedance 

Materials. Experimental Mechanics 1999, 39, 1–5. 

31. Harding, J. Effect of Strain Rate and Specimen Geometry on the Compressive Strength of 

Woven Glass-Reinforced Epoxy Laminates. Composites 1993, 24 (4), 323–332. 

32. Takeda, N.; Wan, L. Impact Compression Damage Evolution in Unidirectional Glass Fiber 

Reinforced Polymer Composites, ASME, AD in High Strain Rate Effects on Polymer, Metal 

and Ceramic Matrix Composites and Other Advanced Materials 1995, 48, 109–113. 

33. Leber, H.; Lifshitz, J. M. Interlaminar Shear Behavior of Plain-Weave GRP at Static and 

High Rates of Strain. Composites Science and Technology 1996, 56 (4), 391–405. 

34. Deltort, B.; Neme, A.; Tanguy, B. New Specimen Geometry for Compression Hopkinson 

Bars. Journal De Physique, IV 1997, 7 (3), C3-265–C3-270. 

35. Ninan, L.; Tsai, J.; Sun, C. T. Use of Split Hopkinson Pressure Bar for Testing Off-Axis 

Composites. International Journal of Impact Engineering 2001, 25, 291–313. 

36. Bertholf, L. D.; Karnes, C. H. Two-Dimensional Analysis of the Split Hopkinson Pressure 

Bar System. Journal of Mechanics and Physics of Solids 1975, 23, 1–19. 

37. Zencker, U.; Clos, R. Limiting Conditions for Compression Testing of Flat Specimens in the 

Split Hopkinson Pressure Bar. Experimental Mechanics 1999, 39 (4), 343–348. 

38. Anderson C. E., Jr.; O’Donoghue, P. E.; Lankford, J.; Walker, J. D. Numerical Simulation 

of SHPB Experiments for the Dynamic Compressive Strength and Failure of Ceramics. 

International Journal of Fracture 1992, 55, 193–208.
34 

39. Lopatnikov, S. L.; Gama, B. A.; Krauthauser, C.; Gillespie, J. W., Jr. On the Classic 

Split-Hopkinson Pressure Bar (SHPB) Analysis. Technical Physics Letters 2004, 30 (2), 

39–46. 

40. Pochhammer, L. Uber Fortplanzungsgeschwindigkeiten kleiner Schwindungen in einem 

unbegrenzten isotropen Kreiszylinder. Journal reine angewandte Mathematik (Creele)

1876, 81, 324. 

41. Ren, L.; Larson, M.; Gama, B. A.; Gillespie, J. W., Jr. Wave Dispersion in Cylindrical 

Tubes: Applications to Hopkinson Pressure Bar Experimental Techniques. International 

Journal of Impact Engineering, submitted for publication, May 2003. 

42. Herrmann, G.; Mirsky, I. Three-Dimensional and Shell-Theory Analysis of Axially 

Symmetric Motions of Cylinders. Journal of Applied Mechanics 1956, 23, 563–568. 

43. Mirsky, I.; Herrmann, G. Axially Symmetric Motions of Thick Cylindrical Shells. Journal 

of Applied Mechanics 1958, 25, 97–102. 

44. Zhao, H.; Gary, G. On the Use of SHPB Techniques to Determine the Dynamic Behavior of 

Materials in the Range of Small Strains. International Journal of Solids and Structures

1996, 33 (23), 3363–3375. 

45. Zhao, H. A Study on Testing Techniques for Concrete-Like Materials Under Compressive 

Impact Loading. Cement and Concrete Composites 1998, 20, 293–299. 
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 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 

COPIES ORGANIZATION COPIES ORGANIZATION

46

 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 

COPIES ORGANIZATION COPIES ORGANIZATION

47

 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 

COPIES ORGANIZATION COPIES ORGANIZATION

48

 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 

COPIES ORGANIZATION

49

 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 
50

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