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Experimental Investigation of the Inelastic Response of Pig and Rat Skin under Uniaxial Cyclic Mechanical Loading

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Cyclic tension tests on pig and rat skin show a strong Mullins effect: irreversible softening plus persistent hysteresis at quasistatic rates, so skin is more inelastic than viscoelastic.

desk verdict A genuinely useful experimental dataset on cyclic skin mechanics, but the paper's central claim that skin is 'more inelastic than viscoelastic' rests on a quasistatic-rate argument that the authors' own relaxation-time citation undercuts. read the letter →

arxiv 1908.06572 v1 pith:VB32ZMY6 submitted 2019-08-19 q-bio.TO

N. Afsar Kazerooni , A. R. Srinivasa , J.C. Criscione This is my paper · ORCID
classification q-bio.TO
keywords Mullinseffectskininelasticityuniaxialcyclicloadingpartialunloadinghysteresiscollagenfiberreorientationstrainratedependencepigandrat
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The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether skin is best described as a viscoelastic solid with full recovery or as an inelastic material with permanent change. By cyclically stretching pig and rat skin with partial unloading at different strain rates and orientations, it establishes that skin shows a strong Mullins effect, an irreversible softening after the first stretch, superimposed on rate-dependent behavior. The key evidence is that substantial hysteresis remains at very slow, quasistatic strain rates, where a purely viscoelastic material would show almost none, and that residual deformation persists for days. A sympathetic reader cares because surgical simulators, injury models, and wearable-device simulations need the first-cycle and partially unloaded response, not just the preconditioned response of a fully recoverable material.

What carries the argument

The central mechanism is the strain-controlled partial-unloading cyclic test, which produces internal loops between the unloading path and the subsequent reloading path; the area of each loop gives the dissipated energy per unit volume. The named phenomenon the paper identifies is the Mullins effect, the irreversible softening and stress reduction that appears after the first loading cycle and is familiar from filled rubber. The paper uses normalized peak stresses to quantify softening, loop areas to quantify hysteresis, and stained histological sections to quantify collagen fiber orientation before and after deformation. Together these measurements connect the macroscopic stress-strain behavior to the microstructural claim that fibers are recruited, reoriented, and left in a permanently straightened configuration.

What would settle it

Run the same cyclic protocol while measuring local surface strain with digital image correlation on the 20 mm by 7 mm dog-bone specimens. If the local strain differs from the grip strain by more than the 5 percent margin reported for the larger validation samples, the reported stress-strain loops, hysteresis areas, and softening percentages would shift by a comparable amount.

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Extended reading notes

Core claim

Under strain-controlled cyclic tension with partial unloading, both pig and rat skin display a pronounced Mullins effect: after the first extension the stress-strain path drops, reloading follows a new path close to but not identical with the unloading curve, and the original response is not recovered on the timescale studied. Softening is larger at higher strain rates and at larger maximum strains, while sample orientation relative to the spine changes stiffness more than it changes the amount of softening. Hysteresis, measured as dissipated energy per unit volume, persists even at strain rates slow enough that the tissue should relax, and specimens retain a permanent stretch after three days of unloading. Histology shows collagen fibers reorient toward the loading direction and stay oriented. From this evidence the paper concludes that skin's response is rate dependent but genuinely inelastic, so purely viscoelastic models cannot capture the first-cycle and partially unloaded response.

Load-bearing premise

The paper assumes that the strain calculated from the testing machine's grip displacement equals the true strain in the middle of each skin specimen, but that equality was checked only on larger, differently shaped samples than the ones used in the reported cyclic tests.

Editorial extensions

If this is right

  • Purely viscoelastic models that recover fully after unloading cannot reproduce the first-cycle response or the reloading paths seen after partial unloading.
  • Constitutive models of skin need internal state variables for permanent softening, fiber reorientation, and residual strain, not just a relaxation spectrum.
  • The reloading path after partial unloading is close to the unloading curve but not identical, giving modelers an additional constraint from the internal-loop shape.
  • Because softening depends more on strain rate than on orientation, experiments and models should report the full loading history and rate rather than only the preconditioned steady-state response.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • One consequence the paper leaves implicit is that preconditioning protocols, which are standard in soft-tissue testing, may be discarding the most clinically relevant part of the response: the first cycle of a fresh tissue.
  • A clean test of the inelasticity claim would be to match loading and unloading rates exactly and make them arbitrarily slow; if the enclosed hysteresis area does not vanish, the residual dissipation cannot be viscous.
  • If the same behavior appears under biaxial stretching, then models for skin grafting, wound closure, and surgical retraction should probably treat the virgin state as the reference state and track permanent set explicitly.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper reports uniaxial cyclic tension experiments on pig and rat skin at different strain rates (0.011 and 0.22 s^-1 for pig; 0.008 and 0.5 s^-1 for rat) and orientations relative to the spine, using strain-controlled partial loading/unloading protocols. The main observations are a large first-cycle softening and hysteresis reminiscent of the Mullins effect in filled rubbers, rate-dependent stress levels, anisotropic stiffening, persistent deformation after unloading that is only partially recovered after three days, and histology showing collagen fiber reorientation. The authors interpret the persistence of hysteresis at their lowest strain rates as evidence that skin is 'more inelastic than viscoelastic' and propose that purely viscoelastic models are insufficient.

Significance. If the central claim were established, the paper would provide useful experimental constraints for constitutive modeling of skin, particularly the need for internal state variables to capture permanent softening and fiber reorientation. The paper's strengths include testing virgin (unpreconditioned) tissue with partial unloading loops, documenting orientation and rate effects, and providing quantitative fiber-orientation histology. These data are potentially valuable to the biomechanics community. However, the paper's main interpretive conclusion - that hysteresis at low strain rates proves inelastic rather than viscoelastic behavior - is not supported by the data as presented, and the quantitative tables are compromised by missing statistics and unexplained negative values. The experimental data themselves may still be publishable if the claims are reframed or the analysis is strengthened.

major comments (3)
  1. [Section 4.2, Conclusions, Table 3] The central inference that persistent hysteresis at the lowest tested rates 'is a marker for inelasticity' is not supported by the data. At 0.008 s^-1 (rat) and 0.011 s^-1 (pig), reaching 60% strain takes about 75 s and 55 s, respectively. The authors themselves cite Eshel and Lanir (ref. 8) with a relaxation time on the order of hundreds of seconds. Thus the loading time is comparable to, not much larger than, the relaxation time, so a purely viscoelastic material would also exhibit substantial hysteresis under this protocol. To claim quasistatic conditions, the loading time should exceed the relaxation time by at least an order of magnitude, or the hysteresis loop area should be shown to approach a nonzero plateau as strain rate decreases. Table 3 instead shows rate-dependent dissipated energy (pig 60% strain: 0.30 MJ/m^3 at 0.011 s^-1 vs 0.18 MJ/m^3 at 0.22 s^-1), which is consistent with viscoelastic rate dependence. In addition, the negative 'dissipated energy' values for rat skin at 0.5 s^-1 (-0.05 to -1.39 MJ/m^3) are never explained; if the reloading curve lies below the unloading curve, the area is not a dissipated energy in the usual sense, and these entries undermine the quantitative basis of the table. The permanent set after three days is separate evidence of damage or inelasticity, but it does not establish that the cyclic hysteresis at the tested rates is inelastic rather than viscoelastic.
  2. [Section 2.2, Appendix (Fig. 11, Table 4)] The validation that crosshead displacement equals local tissue strain was performed on specimens of 54 mm length and 10.4 mm width under monotonic tension, not on the 20 mm by 7 mm dog-bone specimens used in the cyclic tests. The difference between DIC and crosshead strain was reported as less than 5 percent for those larger specimens, but this does not guarantee that the same holds for the smaller cyclic-test specimens, especially under cyclic loading with partial unloading. Since all reported stress-strain curves, hysteresis areas, and softening percentages are computed from crosshead displacement, a systematic difference would shift every quantitative result. Please provide DIC validation on the actual test geometry and loading protocol, or a quantitative argument for why the previous validation transfers.
  3. [Section 2.2, Figures 3-4, Tables 1-3] Only two samples were tested per condition, and no error bars, standard deviations, or statistical comparisons are reported. The statement that tests 'show a repeatable response within the margin of less than 8 percent' is asserted but not documented with per-sample curves or quantitative variability. This is a load-bearing issue for the quantitative claims, such as the 11% versus 15% softening differences at different strain rates and the dissipated-energy comparisons in Table 3. Please provide the individual replicate data or a statistical summary (e.g., mean plus or minus SD) for each condition, and state the number of samples used in each quantitative entry.
minor comments (6)
  1. [Throughout] There are numerous typographical errors, including 'uniaixal' for 'uniaxial', 'mullins' for 'Mullins', 'angel' for 'angle', 'hystereses' for 'hysteresis', and 'an rat skin sample' for 'a rat skin sample'. A careful proofreading pass is needed.
  2. [Introduction, reference [16]] Reference [16] is Lokshin and Lanir, but the text refers to 'Lanir et al. [16]' and contains a sentence fragment ('Lanir et al. [16]. Primarily focused on ...'). This should be corrected to refer to Lokshin and Lanir and edited into a complete sentence.
  3. [Figure 2(b) caption] The caption states that 'positions of the peak and valley coincide showing that, at this slow rate, there is no lag,' but the figure plots stress and strain versus time and it is not clear how 'coincide' is defined or why this demonstrates no lag. Please clarify.
  4. [Table 3] The units in the header ('M J/m3') should be typeset as 'MJ/m^3'. The negative entries for rat skin at 0.5 s^-1 should either be explained in the text or omitted, since a negative 'dissipated energy' requires clarification of the sign convention.
  5. [Section 4.1] The permanent stretch is reported as '3 mm' without reference to the initial gauge length; please report this as a residual strain percentage or with the specimen dimensions so it is meaningful.
  6. [Abstract] The phrase 'the skin response is rate dependent but inelastic' is confusing; 'rate-dependent and inelastic' or 'rate-dependent yet inelastic' would be clearer, since rate dependence and inelasticity are not mutually exclusive.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: direct experimental observations drive the conclusions; self-citations are minor and non-load-bearing.

full rationale

The paper's central claims—Mullins-type softening, persistent hysteresis, rate dependence, permanent set, and fiber reorientation—are supported by direct measurements: force-displacement loops, hysteresis areas computed from measured stress-strain curves, day-0/day-3 retests on the same samples, and histology. No constitutive model is fitted to the data and no quantity is predicted from a fitted parameter; the claim that skin is 'more inelastic than viscoelastic' is an interpretation of measured loop areas and permanent deformation. The references to the authors' own work are (i) the companion modeling paper [13], described as under review/future work and used only to phrase a microstructural narrative ('These observations helped us to model the behavior of skin [13]'), and (ii) the general inelasticity criterion 'hysteresis still exists, which is a marker for inelasticity [31] and [27]'. Neither citation supplies the experimental result, and neither is fitted to, or derived from, the present data. The paper's genuinely weak point is scientific rather than circular: the slowest rates (0.008-0.011 s^-1) give loading times of 55-75 s to 60% strain, comparable to the cited tissue relaxation time of 'hundreds of seconds' [8], so the claim of quasistatic conditions is questionable. That is a validity concern, not a circularity.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted: the paper reports direct strain-controlled measurements. Interpretive claims rest on external literature for relaxation time and incompressibility, and on the grip-strain equivalence assumption noted above.

assumptions (5)
  • domain assumption Grip displacement strain equals gauge-section strain within 5%.
    Used for all stress-strain curves in Section 3; validation in the Appendix used different specimen geometry (54 mm x 10.4 mm) than the cyclic test specimens (20 mm x 7 mm).
  • domain assumption Skin is nearly incompressible.
    Invoked when converting to true stress and logarithmic strain (Figure 5c-e); based on North and Gibson 1978.
  • domain assumption Relaxation time of rat dorsal skin is on the order of hundreds of seconds.
    Quoted from Eshel and Lanir 2001 and used in Section 4 to classify 0.008-0.011/s as slow rates.
  • domain assumption Cold storage at 0 C for 3 days does not alter the mechanical response except for prior cyclic loading.
    Used to attribute the day-3 softening to cyclic damage; supported by control samples in Figure 6a-b, but n=1 per control.
  • domain assumption The cyclic loading protocol does not tear the tissue.
    The interpretation as Mullins effect, rather than fracture, assumes that the observed softening is not due to tearing; the paper states that unloading occurs before tearing but does not verify this for every sample.

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Pith. "Pith review of Experimental Investigation of the Inelastic Response of Pig and Rat Skin under Uniaxial Cyclic Mechanical Loading." pith.science (2026). https://pith.science/paper/VB32ZMY6

@misc{pith2026190806572,
  author       = {Pith},
  title        = {Pith review of: Experimental Investigation of the Inelastic Response of Pig and Rat Skin under Uniaxial Cyclic Mechanical Loading},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VB32ZMY6}},
  note         = {Machine review of arXiv:1908.06572}
}
read the original abstract

Skin is a highly non-linear, anisotropic, rate dependent inelastic, and nearly incompressible material which exhibits substantial hysteresis even under very slow (quasistatic) loading conditions. In this paper, a series of uniaxial cyclic loading tests of porcine and rat skin at different strain rates and with samples oriented in different directions (with respect to the spine) were conducted to study the effect of strain rate and samples orientations with respect to spine on mullins effect and skin inelastic response. A noteworthy feature of skin is that, similar to certain filled rubbers, its mechanical response shifts after the first extension and exhibits softening and hysteresis when loaded under cyclic tension and mullins effect is observed. The results of these strain-controlled cyclic loading tests also indicated that the extent of softening is different for different strain rates and orientations. Also a substantial hysteresis persists even at very low strain rates indicating inelastic behavior beyond the rate sensitive viscoelastic response. Through this series of experiments, by investigating the effect of strain rate on pig skin and rat skin, we conclude that the skin response is rate dependent but inelastic and shows irreversible changes in fiber orientation which are observed in histology results. Also, skin shows persistent deformation that is only partially recovered even after a long period of unloading.

Figures

Figures reproduced from arXiv: 1908.06572 by the authors.

Figure 1
Figure 1. a) Pig skin sample in wedge action grips, b) The pig skin dog bone specimen, [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. a) Displacement path of uniaxial partially loading and unloading tension [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Cyclic uniaxial tension testing of pig skin at different directions. Also, it [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Cyclic uniaxial tension testing of rat skin at different directions. Also, it [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: The effect of samples direction with respect to spine (a-b): comparison of [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Uniaxial cyclic loading testing until 60 percent strain at the strain rate [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: A) Optical microscopic images of the surface of outer layer of pig skin dog [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Microstructure of samples after staining: before deformation (sample 0) [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: Fiber distributions of control sample with no deformation (sample 0) and [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: a) Standard deviation over fiber distribution and b) Maximum probability [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: a) Schematic calculation of Engineering Strain in Y direction from DIC. [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]

Discussion (0). Continue with ORCID to comment.

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