dynamic tensile characterization of pig skin

Acta Mechanica Sinica (2014) 30(2):125132DOI 10.1007/s10409-014-0042-9

RESEARCH PAPER

Dynamic tensile characterization of pig skin

H. Khatam Q. Liu K. Ravi-Chandar

Received: 23 January 2014 / Accepted: 20 March 2014The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag Berlin Heidelberg 2014

Abstract The strain-rate dependent response of porcineskin oriented in the fiber direction is explored under ten-sile loading. Quasi-static response was obtained at strainrates in the range of 103 s1 to 25 s1. Characterization ofthe response at even greater strain rates is accomplished bymeasuring the spatio-temporal evolution of the particle ve-locity and strain in a thin strip subjected to high speed impactloading that generates uniaxial stress conditions. These ex-periments indicate the formation of shock waves; the shockHugoniot that relates particle velocity to the shock velocityand the dynamic stress to dynamic strain is obtained directlythrough experimental measurements, without any assump-tions regarding the constitutive properties of the material.

Keywords Nonlinear waves Impact tests Digital imagecorrelation Shocks Hugoniot

1 Introduction

The dynamic mechanical behavior of soft materials such asrubbers, elastomers, gels, and biological tissues has attractedmuch attention in recent years; this is driven by the need fordetermining accurate strain-rate dependent constitutive mod-els that are used in modeling the response to impact, penetra-tion and other modes of loading in structural applications aswell as biomechanical applications. In this article, we focuson pig skin and its dynamic response. The split-Hopkinsonbar apparatus has evolved into the most common method fordynamic material characterization (see for example, the re-view of the technique by Subhash and Ravichandran [1]); itsuse has been well-established for a range of materials. Themain advantage of this technique is that it does not use adetailed analysis of wave propagation through the specimenmaterial and therefore a priori knowledge of the material be-

H. Khatam Q. Liu K. Ravi-Chandar ()Center for Mechanics of Solids,Structures and Materials,The University of Texas at Austin, USAe-mail: [email protected]

havior is not required. However, the assumptions of unifor-mity of the stress and deformation within the specimenwhich are needed for interpretation of the experimentsthrough elementary analysisplace rather severe restric-tions on the specimen size, strain rates, and strain levels thatcan be obtained and limit the applicability of this techniqueto a certain class of materials and certain range of strain rates.For tension testing, the specimens need to be quite small(for example on the order of one or two millimeters); whilethe strain rates obtained are typically in the range of about102103 s1, the duration of loading is small, and hence thestrain levels achieved are quite small. The technique is bet-ter suited for compression characterization, with strain ratesreaching nearly 104 s1. The measurement of strain-rate de-pendent tensile behavior of soft materials with a Hopkinsonbar, particularly for large stretch levels, is fraught with diffi-culties; in addition to the problems arising from impedancemismatch with the loading bars that causes a very low signalto noise ratio, lateral inertia effects in the specimen and thegeneral inhomogeneity of the stress and deformation in thistest scheme provide very restrictive conditions under whichthe split Hopkinson bar may be used in tension. Furthermore,for applications in many soft materials, very large stretch lev-els are encountered; this necessitates long duration pulses for example, to reach a stretch ratio of two at a strain rate of103 s1, a pulse duration of 2 ms is required! In order to over-come such limitations, we have used an experimental methodfor dynamic tensile characterization of materials using tran-sient wave propagation (Niemczura and Ravi-Chandar [24]and Albrecht et al. [5]) and shock wave analysis (Niemczuraand Ravi-Chandar [3]). In the present work, we apply thesetechniques, along with some variants that allow lower strain-rate ranges to be achieved, to examine the dynamic responseof pig skin.

This paper is organized as follows: the quasi-static re-sponse of pig skin is discussed in Sect. 2 to provide the un-derlying characterization that is used as the basis for com-parison of the dynamic response. This is followed in Sect. 3by a description of one dimensional wave propagation as the

126 H. Khatam, et al.

basis for interpreting the high strain-rate experiments. Inparticular, the theoretical background that is necessary forthe interpretation of the experiments is discussed. The re-sults of these experiments are examined in Sect. 4 to explorethe shock response and to construct the shock Hugoniot. Asummary of conclusions and a perspective of soft materialcharacterization are provided in Sect. 5.

2 Quasi-static mechanical response of pig skin

Pig skin is the material considered in the present investi-gation of the strain-rate dependence of the constitutive re-sponse. Skin is a connective tissue, but with one significantdifference from other connective tissues: it is a protectivebarrier material, for which one side is always subjected tothe ambient environment. The general practice in tissue test-ing is to place the specimen inside a hydration bath in orderto maintain the specimen at physiological temperature andfurthermore, to avoid excessive drying (dehydration). How-ever, the compromise in this process is that the sample willabsorb some water and may exhibit a non-native response,mediated by the swelling. Obviously, skin in physiologi-cal condition is not fully immersed inside a liquid and thein-vivo mechanical properties may vary from those obtainedfrom an overhydrated skin sample [6]. Another importantfactor in determining the mechanical response of soft tis-sues is the strain-rate dependence. Although the responseis expected to become less sensitive to strain rate at very lowstrain rates [7], this requires very long loading and immers-ing time which inevitably leads to an overhydrated sample.Finally, studies (for example, Ref. [8]) have demonstratedthat in normal conditions and under clothing, the tempera-ture of human skin in most parts of the body is considerablybelow the typically imposed physiological body temperature(37C) and is in the range of 28C to 35C with an averagetemperature of 33C.

For the tests performed in this work, a large cut of pork-belly was obtained from a local abattoir, and after removingthe muscle and subcutaneous layer, the skin was preparedand tested within 48 hours post-mortem. Samples from theabdominal area were cut along the longitudinal and trans-verse axes to uniform width (56 mm); only the results ofspecimens oriented along the longitudinal or fiber directionare reported in this article. The measured density was be-tween 1.100 and 1.160 g/cm3, and skin thickness varied be-tween 2 and 3 mm. Three different experimental arrange-ments are considered in this work in order to obtain the re-sponse of pig skin. All tests were conducted in room tem-perature (25C). We demonstrated, in previous work [9],the dramatic effect of water content on the quasi-static re-sponse of pig skin. For the current tests, samples were keptin a closed container in the presence of saline-soaked papertowels until testing. After removing a sample from this mois-ture chamber, the mounting and test were performed within5 minutes.

The first test was performed in an Instron universal test-

ing machine at strain rates in the range of 103 s1 and theother two involve one dimensional impact loading. In thefirst type of impact experimental arrangement, strain rates inthe range of 10 s1 are achieved; in these experiments, theforce on the specimen is measured directly with a piezoelec-tric load cell. In the second type of impact experiment, shockwaves are generated necessitating direct measurements ofparticle velocities and strains in order to enable determina-tion of the forces.

2.1 Low strain-rate experiments

Specimens of width 5 mm, thickness 2 to 3 mm, and length4 cm were pulled in uniaxial tension in an Instron test-ing machine at a cross-head speed of 0.3 mm/s resultingin an average strain rate of 0.007 s1. In order to providea good gripping boundary condition, self-tightening gripswere used; even in this case, some portion of the specimenoutside the gage length of the specimen experiences strainsand therefore, reliance on global displacement measurementwould overestimate the actual local strains experienced bythe specimen. Therefore, the digital image correlation (DIC)technique was used to measure the local strains and thencorrelated to the measured average stress in order to extractthe nominal stress vs. nominal strain variation. The result-ing stressstrain curve is shown in Fig. 1 as the solid blackline. At about a strain level of 0.4, the specimen began toslip in the grips and the test could not be continued further.However, the characteristic response of pigskin is capturedin this test. It is easy to see that the initial stiffness, cor-responding to unkinking the crimped collagen structure isquite small. The initial tangent elastic modulus (for strainlevels below about 0.2) is around 1 MPa. However, uponstraightening of the collagen kinks, the linear part of the re-sponse has a considerably higher tangential elastic modulusaround 100 MPa beyond a strain level of about 0.4. Althoughnot shown here, the primary difference between the fiber di-rection and the transverse direction lies in the fact that thestiffening response is seen at much larger strain level whentested in the transverse direction. Exact comparison of theseresults to previous work is difficult for two reasons: first, theidentification of the reference configuration contains signif-icant error; therefore matching the strain level at which sig-nificant stiffening occurs is difficult. Second, handling, mois-ture content, and temperature influence the response signif-icantly. Therefore, comparisons can only be in terms of or-der of magnitude of the quantities of interest. Ankersen etal. [10] used 30 mm wide pig skin specimens with a dumb-bell shaped ends and reported a stressstrain response similarto that shown in Fig. 1. Maximum stress levels at failure is inthe order of 1030 MPa and strain levels at failure of about0.240.29 are reported; the present results are comparable tothese results, although the failure strain levels are somewhatlarger in the present work. In contrast, Lim et al. [11], whoalso tested pigskin under low strain rates, reported uniaxialstress strain curves that were significantly different; in factat a strain level of about 0.35, the stress indicated by Lim et

Dynamic tensile characterization of pig skin 127

al. [11] is around 30 kPa, whereas the present results indi-cate about 10 MPa. The likely reasons for these differencesare not known, but for consistency and minimization of sam-ple to sample variability, we shall compare the stressstraincurves obtained at different strain rates from the same ani-mal, prepared and tested as indicated above.

Fig. 1 Nominal strain vs. nominal stress variation for pig skin. Thesolid line indicates the response of a test performed in an Instrontest machine at a strain rate of 0.007 s1. The two other sets ofsymbols (, ) correspond to the response from low-speed impacttests at two different intermediate strain rate tests (17 and 23 s1)discussed in Sect. 2.2

2.2 Intermediate strain-rate experiments

The specimens used in the intermediate strain rate experi-ments are about 175200 mm long and 56 mm wide; afterremoval of the subcutaneous fat layer with a surgical scalpel,the specimens were about 23 mm thick. The specimen iswrapped around a slider illustrated in Fig. 2, with the sliderinserted into the slotted muzzle of an air-gun, and the twoends of the specimen are clamped to a piezoelectric loadcell, providing a minimum gage length of about 20 mm. Thespecimen is decorated with a random pattern of dots with anindelible ink to facilitate determination of the deformationusing digital image correlation. One dimensional loading isapplied by impacting the specimen holder with an 880 mmlong projectile driven from the air-gun at a speed of about1 m/s. A Photron SA1 high-speed video camera, operatedat 5 000 frames per second, is used to capture the deforma-tion of the specimen upon impact. The entire process is syn-chronized by a controller: upon sending a command signal,this system provides a trigger to the solenoid valve for theair gun, and a trigger with suitable delays to begin record-ing the high speed camera images and the oscilloscope forthe load cell data. The details of two tests in the fiber direc-tion are provided here. The strain field was obtained from

the images using the commercial DIC program ARAMIS.Stress waves propagate back and forth between the impactpoint and the fixed grip at the load cell, and establish uni-form strain conditions in the central 10 mm of the specimen.Figure 3 shows the time variation of the strain at a point inthe center of the specimen in two different tests. In the firsttest, the specimen was held tight in the loading fixture andresulted in a constant strain rate of 23 s1, while in the sec-ond specimen, an initial slack in the specimen holder delayedthe start of straining, and resulted in a small variation in thestrain rate, ending up at about 17 s1. The correlation of thestrain measurement with the load measured with the piezo-electric load cell yields the dynamic stressstrain curve forstrain rates in the range of 1723 s1; this is shown in Fig. 1as the filled and open circular symbols. The comparison tothe quasi-static stress strain curve indicates that the shape ofthe stressstrain curve does not vary significantly with thechange in strain rate over four orders of magnitude, but that

Fig. 2 Diagram of the slider; the specimen is wrapped around theslider in the groove on the cylindrical surface of the half-disk. Theslider is then inserted into the slotted muzzle of an air gun. The twoends of the specimen are then clamped either to the piezoelectricload cell or to the exterior of the barrel itself

Fig. 3 Time variation of the nominal strain in the gage section forthe intermediate strain-rate experiments. The difference betweenthe two tests arises from the initial slack or tension in the specimenwhen placed in the impact apparatus

In fact, translating the stressstrain curve at the intermediate strain rate along the strain axis, we observed nearly perfect overlap of thequasi-static and intermediate strain rate responses.


the stiffening response is observed at smaller overall strainlevels than in the lower strain rate experiments. It should benoted that there is some uncertainty in the reference configu-ration which could result in a strain uncertainty, and henceshifting of the stress strain curve along the strain axis isa possibility that can not be completely eliminated. How-ever, the initial stiffness in the intermediate impact range(evaluated at strain levels below 0.2) suggests an increaseto about 2.5 MPa. Next, we consider even higher impactspeeds, where wave propagation effects need to be investi-gated.

3 Shock wave analysis and Hugoniot construction

Consider a semi-infinite specimen of width D and thicknessh occupying x > 0; at t = 0, the end x = 0 is impacted by aprojectile traveling at a speed Vp in the negative x direction,and imposes a particle velocity V Vp; this generates aone dimensional wave that propagates into the specimen. Ifthe transverse deformation is small, inertia effects associatedwith the transverse motion may be neglected and one may as-sume one-dimensional motion of material points; the presentexperiments provide an opportunity to explore this aspect.Under such conditions, the subsequent motion of materialpoints in the specimen is represented completely by a singlekinematic quantity, u(x, t), the displacement in the x direc-tion; therefore, the current position of the material point x atany time t is given by y(x, t) = x+u(x, t). The correspondingstrain and particle velocity are given by (x, t) = u/x andV(x, t) = u/t, respectively. Soft materials such as elas-tomers and rubbers are usually assumed to be incompress-ible; for biological tissues, the presence of moisture and theresulting pore pressure may need to be taken into account,but this will not be explored in the present work. The equa-tions governing the balance of mass and momentum can bewritten down as

Vx=

t,

x= 0Vt, (1)

where is the nominal stress and 0 is the mass densityper unit volume. These equations are obtained from basicbalance laws and are therefore applicable to any material.Therefore, in order to complete the formulation for a specificmaterial, we must specify the material behavior; this is thefield of constitutive theory. This system of equations is com-pleted by the addition of an equation of state; for example,for an elastic material this can be represented by the specificinternal energy U() in terms of the strain . This bringsthe connection between the stress and strain: = 0U/.Note that thermal effects have been neglected in this formu-lation, but this is adequate for the experiments consideredhere since temperature changes due to deformation may beconsidered to be negligible. Solutions that are continuousand differentiable can be obtained for some constitutive mod-els; there are numerous investigations of compressive wavepropagation in nonlinear solids [1216]. There has been rel-atively little work on tensile waves [2, 5, 1721] that examine

propagation of finite amplitude waves.In order to explore the wave propagation in pig skin in

view of the stressstrain relations, () obtained in the pre-vious section, we express Eq. (1) in terms of the particle dis-placement to obtain the nonlinear wave equation in familiarform

[c()]22ux2=2ut2, (2)

where c() =()/, is the speed (in the reference con-

figuration) of incremental waves propagating in a specimenstrained to a level with the prime indicating a derivativewith respect to the argument. Suitable initial conditions needto be specified; for example, the initial strain and particle ve-locity along the specimen can be prescribed: (x, 0) = g(x),v(x, 0) = h(x). For a given constitutive response, this corre-sponds to specifying the initial stress state as well. The gen-eral solution to this boundary-initial value problem can beobtained analytically for some forms of the stress strain re-sponse () (see Ref. [20]), while numerical schemes suchas the method of characteristics must be used in other cases(see for example, Ref. [2]).

Bethe [22] examined conditions under which discontin-uous solutions are possible for materials with arbitrary equa-tion of state and showed that stable shocks are possible when

02

2> 0. (3)

Such discontinuities are called shocks, and a vast, classicalliterature exists that explores the generation and propaga-tion of shocks, characterizes the response of materials undershock conditions, and examines the development of modelsfor the equation of state. The classical book by Zeldovichand Raiser [23] and the more recent book by Davison [24]provide a summary of shock propagation in solids. In orderto account for such discontinuities where the derivatives arenot defined, the governing differential equations in Eq. (1)have to be rewritten in terms of the jumps across the discon-tinuities or shocks. Let the shock occur at x = s(t) and letus denote the Lagrangian shock speed as s; then these jumpconditions can be written as

s[[]] + [[V]] = 0, 0 s[[V]] + [[]] = 0, (4)

where [[g]] = g(s+(t), t) g(s(t), t) is the jump operator,which is defined as the relevant parameter ahead of theshock (superscript +) minus that same parameter behindthe shock (subscript ). If we consider that the shock ispropagating into an undisturbed medium, the + states arequiescent and Eq. (3) represent two equations (representingmass and momentum balance) that govern four unknowns(, , V, and the shock speed s). Typically, one of thequantities behind the shockeither the particle velocity V

or the stress is imposed as a boundary condition. Theother must be provided either through another measurementor through an appropriate constitutive law: (); herein liesthe crux of the problem! How does one get the appropri-


ate constitutive law? There are two approaches: the experi-mental approach is to use a direct measurement of the shockspeed and construct diagrams of the variation of the shockspeed with impact speed. The diagram of the shock speedvs. impact speed is called a shock Hugoniot. Such a shockHugoniot curve must be characterized for each initial state;the Hugoniot corresponding to the quiescent initial state iscalled the Principal Hugoniot. It is not a complete mate-rial constitutive characterization, but is sufficient to performcalculations of shock effects. The second approach is to de-termine an equation of state through lower scale models ofdynamic material response, and then to establish the Hugo-niot curve analytically. In the present work, we focus ondetermining the principal Hugoniot for pig skin experimen-tally.

For the case of pig skin, we use the experimentally de-termined stress strain curve shown in Fig. 1 for the interme-diate strain rate tests, and obtain the variation of the wavespeed c() =

()/; the result is shown in Fig. 4. We

note that for small strain levels, < 0.14, the wave speedis nearly constant at 43 m/s (to within experimental accu-racy in determining the stressstrain curve in the low stiff-ness region). For larger strain levels > 0.14, the wavespeed increases rapidly with strain. The interpretation of thisstrain-dependence of the wave speed is as follows: any straindisturbance with magnitude < 0.14 will propagate into thespecimen with a speed of 43 m/s. For > 0.14, greater strainlevels will move faster than lower strain levels indicating theformation of a shock wave. In other words, the Bethe condi-tion in Eq. (3) is satisfied for > 0.14, and shock waves canform.

Fig. 4 Dependence of the wave speed on strain level. In the ini-tial region ( < 0.14), the wave speed is nearly independent of thestrain, but beyond 0.14, there is a significant increase causedby the stiffening response of the material

4 High strain-rate experiments

Higher strain-rates than that indicated in Sect. 2 were ob-tained by impacting the specimen with a shorter projectile(2.5 cm long) driven to higher speeds (in the range of 8 to

37 m/s); the main difference from the experiments describedin Sect. 2.3 is that the two ends of the specimen are clampeddirectly to the gun-barrel without the piezoelectric load cell,because the frequency response of the piezoelectric load cellis insufficient to provide force measurement in this experi-ment. However, this inability to measure the force directlyis not a serious impediment since we may use shock jumpanalysis in Sect. 3 to extract the stress in the specimen. Sincethe impact speeds are high, and the response times short,the high speed camera was set to capture images at 50 000frames per second or intervals of 20 s. Other elements ofthe experiment are as indicated above. The details of onetestcorresponding to an impact speed of 16.6 m/swiththe specimen oriented in the fiber direction are providedhere.

(1) Selected frames from the high speed image se-quence with an overlay of the strain field as determined byDIC are shown in Fig. 5; the time interval between the im-ages is 80 s. These results provide a number of importantobservations regarding the deformation. In the first two im-ages (the first 80 s), the projectile has impacted the flangeand begins to move, but there is no indication of deformationin the specimen; in the third image (160 s), the strain pulseis seen to move into the field of view. In the fourth image(at 240 s), while there is a significant amount of strain onthe impact side, the right side of the specimen is completelyunstrained. There appears an abrupt jump in the strain from = 0 to over a small spatial extent (because of er-rors in the strain measurement that arise due to the unknowninitial configuration, we will determine the strain level fromconservation of mass, rather than from direct kinematic mea-surements). With time, the location of the strain jump movesto the right along the specimen. This indicates that in re-sponse to high speed impact, a wave is developed, acrosswhich the specimen experiences a jump in strain as well asparticle velocity.

(2) The time variations of the displacement, particle ve-locity and strain at four selected points along the specimen,labeled as stage point n (n = 0, 1, 2, 3) in Fig. 5, are shown inFig. 6. Prior to the arrival of the wave, the specimen is in anunloaded state: (+ = 0, V+ = 0). Upon arrival of the waveat any point, the particle velocity and strain increase rapidlyand attain a constant value: V = 16.6 m/s and ,respectively.

(3) The position of the strain jump moves along thespecimen with a speed s which can be estimated from prop-agation of a constant level of strain into the material; in thepresent experiment, the speed of propagation of the strainlevel of 0.80 was used to find s = 105.2 m/s. Notethat this is larger than the elastic wave speed of 43 m/s cor-responding to strain levels < 0.14.

(4) Since the material is initially at rest, the stress, strainand particle velocity ahead of the shock are zero and thejump conditions in Eq. (4) can be used to write the strain andstress behind the shock as follows


Fig. 5 Sequence of high speed images (0.08 ms time interval) of the pig skin specimen subjected to one-dimensional impact at a speedof approximately 16.6 m/s. The red dashed line indicates the motion of the front end of the specimen holder. The yellow line indicates apoint on the specimen, just outside of the holding flange; the position variation of this point is used to calculate the particle velocity in thespecimen. The strain field calculated from digital image correlation is overlaid on the physical image of the specimen decorated with aspeckle pattern. The strain propagates into the specimen, towards the fixed end at a speed of approximately 105 m/s, significantly greaterthan the small-stretch elastic wave speed of 43 m/s. For scale, the specimen initial width is 6.5 mm

Fig. 6 Time variation of the particle displacement, particle velocity,and strain at four points identified in Fig. 5 as stage points 0 through3. The coordinates of the stage points are: x3 = 0, x2 = 6.3 mm,x1 = 12.6 mm, x0 = 18.9 mm

= V/s, = 0 sV. (5)

The particle velocity, V = 16.6 m/s, is imposed by theprojectile impact and has been measured. The speed of prop-agation of the strain jump, s = 105.2 m/s, has also been mea-sured directly. Therefore, the strain and stress behind thejump can be calculated from Eq. (5). For this experiment,we get ( = 0.16, = 1.92 MPa).

Similar experiments were performed on other speci-mens obtained from the same animal from neighboring lo-cations and different impact speeds. The measured values ofV and s are shown in Table 1; these are used subsequentlyin Eq. (5) to determine the strain and stress levels behind theshock that are indicated in the 3rd and 4th columns of Table1. These values of strain and stress form the principal Hugo-niot for pig skin. From Eq. (5), it is clear that it is sufficientto identify the pairs (V, s) in order to identify the Hugo-niot; this relationship is shown in Fig. 7 and appears to benearly linear over the range of impact speeds considered. A


linear V s Hugoniot of this type has been observed formost solids (see Zeldovich and Raiser, 2002 [23]) and is ex-pressed as

s = C0 + S V. (6)

A least-squares fit to the data yields C0 = 50 m/s and S = 4.3(with R2 = 0.82) and is also shown in Fig. 7. The constantsC0 is usually given physical interpretation (see Zeldovichand Raiser, 2002 [23]) based on the limit as V 0. Thelimit for s as V 0 should be the wave speed correspond-ing to small strain levels; it is observed that, indeed, the valueof C0 = 50 m/s is close to the wave speed of 43 m/s estimatedin Sect. 3 for < 0.14. It is also instructive to consider theprincipal Hugoniot in terms of the stress and stain: (, );these are the end states achieved through impact and are plot-ted in Fig. 8; for comparison, the quasi-static and intermedi-ate strain-rate stressstrain curves are also shown. It is clearthat the stressstrain states reached through impact are sig-nificantly different from those attained through quasi-staticloading. The line connecting the quiescent initial state andthe shock end state, illustrated with one example in Fig. 8, iscalled the Rayleigh line. The slope of this line is proportionalto the square of the shock speed, and the area underneath thisline gives an estimate of the energy expended in straining tothe level behind the shock.

Table 1 Impact test results indicating impact speed, shock speedand the corresponding stress and strain levels behind the shock

Test Impact speed Shock speedStrain Stress/MPa

ID V/(ms1) s/(ms1)F 20 8.1 73.3 0.11 0.65

F 40 16.6 105.2 0.16 1.92

F 60 20.0 171.4 0.12 3.77

F 80 20.9 147.6 0.14 3.39

F 100 37.3 199.8 0.19 8.20

Fig. 7 The V s Hugoniot for pig skin. The dashed line corre-sponds to a linear fit to the experimental data: s = 50 + 4.3V withR2 = 0.82

Fig. 8 The principal Hugoniot (pentagram symbols) for pig skinin the fiber orientation is shown in comparison to the intermediate(, symbols) and static stressstrain response (solid line). TheRayleigh line for one of the impact tests is shown by the arrowwhich indicates the shock jump from a quiescent initial state to anend state that is quite far away from the low and intermediate re-sponse. For the same strain level, the stress attained under shockconditions is substantially greater

In closing, we note a few points for further considera-tion: first, the Hugoniot determined in the present work cor-responds to the fiber direction orientation of the specimen;similar characterization must be performed in the transversedirection. Second, we have only examined the initial pulsepropagation into the material; at longer times, the continuedmovement of the projectile and the finite dimensions of thespecimen result in further straining and eventual failure ofthe specimen at high strain-rates; these have not been ana-lyzed. Third, the maximum particle speed considered was37 m/s; extension of the Hugoniot to higher impact speedsshould be considered. Finally, while we have interpreted themeasurements through the jump equations, and constructedthe shock Hugoniot, the finite rise time of the strain pulseseen in Fig. 6 suggests that it may be possible to postulate aviscoelastic or viscoplastic constitutive model for the mate-rial and analyze the results using the propagation of a steady-wave (see Ref. [24]).

5 Conclusion

The quasi-static and dynamic mechanical response of pigskin specimens were determined through uniaxial tensionand one-dimensional wave propagation experiments. Thequasi-static mechanical response of pigskin in the fiber ori-entation, when strained at rates of about 103 s1 was ob-tained in an Instron test machine. Higher strain rates (in therange of 10 to 25 s1) were obtained through projectile im-pact on a short strip of specimen at speeds of about 1 m/s.High speed photography and digital image correlation wereused to determine the strain variation over a few millisec-onds; a piezoelectric load cell, with adequate frequency re-sponse, was used to identify the force. The resulting charac-terization of the stressstrain response indicated that the ef-


fect of the strain-rate is to bring the stiffening portion of thestressstrain curve to smaller strain levels. Characterizationof the response at even greater strain rates is accomplished bymeasuring the spatio-temporal evolution of the particle ve-locity and strain in a thin strip subjected to high speed impactloading that generates uniaxial stress conditions. These ex-periments indicate the formation of shock waves; the shockHugoniot that relates particle velocity to the shock velocity,and the dynamic stress to dynamic strain is obtained directlythrough experimental measurements, without any assump-tions regarding the constitutive properties of the material.Interestingly, a linear relation between the impact speed andthe shock speed was observed, as is typical for many materi-als.

References

1 Subhash, G., Ravichandran, G.: Split Hopkinson pressure bartesting of ceramics. In: ASM Handbook, Mechanical Testingand Evaluation. Volume 8, ASM International, 497504 (2000)

2 Niemczura, J., Ravi-Chandar, K.: On the response of rubbersat high strain rates: I: Simple waves. J. Mech. Phys. Solids 59,423441 (2011)

3 Niemczura, J., Ravi-Chandar, K.: On the response of rubbersat high strain rates: I: Shock waves. J. Mech. Phys. Solids 59,442456 (2011)

4 Niemczura, J., Ravi-Chandar, K.: On the response of rubbers athigh strain rates: I: Effect of hysteresis. J. Mech. Phys. Solids59, 457472 (2011)

5 Albrecht, A.B., Liechti, K.M., Ravi-Chandar, K.: Characteri-zation of the transient response of polyurea. Exp. Mech. 53,113122 (2013)

6 Jemec, G.B., Jemec, B., Jemec, B.I., et al.: Effect of superficialhydration on the mechanical properties of human skin in vivo.Plastic Reconstructive Surgery 85, 100103 (1990)

7 Fung, Y.C.: Mechanical Properties of Living Tissues. (2ndedn). Springer (1993)

8 Benedict, F.G., Miles, W.R., Johnson, A.: The temperature ofthe human skin. Proc. Natl. Acad. Sci. USA 5, 218222(1919)

9 Khatam, H., Ravi-Chandar, K.: On the evaluation of the elas-tic modulus of soft materials using beams with unknown initialcurvature. Strain 49, 420430 (2013)

10 Ankersen, J., Birkbeck, A.E., Thomson, R.D., et al.: Punctureresistance and tensile strength of skin simulants. Proc. Instn.Mech. Engrs. 213, 493501 (1999)

11 Lim, J., Hong, J., Chen, W.W., et al.: Mechanical response ofpig skin under dynamic tensile loading. Int. J. Impact. Eng.38, 130135 (2011)

12 Rakhmatulin, K.A.: Propagation of an unloading wave. PriklMatematikai Mekhanika 9, 91100 (1945) (in Russian)

13 Taylor, G.I.: The plastic wave in a wire extended by an impactload. In: The Scientific Papers of G. I. Taylor, Vol. I., Mechan-ics of Solids, University Press, Cambridge, 467479 (1958)

14 Kolsky, H., Douch, L.S.: Experimental studies in plastic wavepropagation. J. Mech. Phys. Solids 10, 195223 (1962)

15 Goldsmith, W.: Impact: The Theory and Physical Behaviour ofColliding Solids. Dover Edition, USA (2001)

16 Clifton, R.J.: Plastic waves: Theory and experiment. In:Nemat-Nasser, S. ed. Mechanics Today, Volumn 1, PergamonPress, Inc, Oxford, 102168 (1973)

17 von Karman, T., Duwez, P.: The propagation of plastic defor-mation in solids. J. App. Phys. 21, 987994 (1950)

18 Mason, P.: Finite elastic wave propagation in rubber. Proc.Roy. Soc. London. Series A, Math. Phys. Sci. 272, 315330(1963)

19 Kolsky, H.: Production of tensile shock waves in stretched nat-ural rubber. Nature 224, 1301 (1969)

20 Knowles, J.K.: Impact-induced tensile waves in a rubberlikematerial. SIAM J. App. Math. 62, 11531175 (2002)

21 Roland, C.M., Twigg, J.N., Vu, Y., et al.: High strain rate me-chanical behavior of polyurea. Polymer 48, 574578 (2007)

22 Bethe, H.: On the theory of shock waves for an arbitrary equa-tion of state. Report No. 545 for the Office of Scientific Re-search and Development, Serial No. NDRC-B-237 (1942); re-produced in: Johnson, J.N., Cheret, R., eds. Classic Papers inShock Compression Science, Springer, USA, 421492 (1998)

23 Zeldovich, Y.B., Raiser, Y.P.: Physics of Shock Waves andHigh-Temperature Hydrodynamic Phenomena. Dover Edition,USA (2002)

24 Davison, L.: Fundamentals of Shock Wave Propagation inSolids. Springer, German (2008)