Canceling the elastic Poynting effect with geometry

J. Blackwell; M. Destrade; N. Colgan; V. Balbi; Y. Du

REVIEW 2 major objections 5 minor 19 references

Canceling the elastic Poynting effect with geometry

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Geometry alone reverses the Poynting effect in soft blocks, and a cube always does, for every material in the third-order theory of weakly nonlinear elasticity.

desk verdict A plausible geometric reversal of the Poynting effect, with a universal cube claim that outruns its evidence. read the letter →

arxiv 2506.03821 v1 pith:44PXFI6W submitted 2025-06-04 cond-mat.soft

M. Destrade , Y. Du , J. Blackwell , N. Colgan , V. Balbi This is my paper

classification cond-mat.soft MSC 74B2074S05

keywords PoyntingeffectsimpleshearhyperelasticityMooney-Rivlinmodelaspectratiosoftsolidsnormalstressfiniteelementsimulation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Every incompressible, isotropic, hyperelastic solid feels the Poynting effect in simple shear: when a block is sheared between parallel plates, it tends to thicken, so a normal force must be applied to keep its height fixed. The paper shows that this effect can be canceled and even inverted purely by changing the block's aspect ratio, with no change of material. Silicone experiments on thin rectangular cuboids show the classical positive normal force, while identical-material cubes show a negative normal force, meaning the block pulls the platens together. Finite-element calculations across Mooney–Rivlin materials produce a critical height-to-length ratio where the normal force vanishes, and the paper's strongest conclusion is that cubes always lie on the reverse-Poynting side for every material in the third-order theory of weakly nonlinear elasticity. If true, this gives a simple geometric design rule for suppressing unwanted vertical forces in sheared soft components such as seismic isolation bearings.

What carries the argument

The load-bearing object is the cuboid aspect ratio $H/L$ and the deviation from idealized homogeneous simple shear. In the infinite-slab theory the deformation is uniform and the normal stress is $\sigma_{22}=-2(\partial W/\partial I_2)K^2$, which always gives the classical positive normal force in the Mooney–Rivlin class; finite blocks have free slanted faces that bend, making the deformation inhomogeneous and changing the integrated normal reaction on the platen. The paper scans the material parameter $\beta=(C_2-C_1)/(C_1+C_2)\in[-1,1]$, which by the third-order equivalence covers all incompressible isotropic hyperelastic solids at small-but-finite strain, and uses finite-element solutions to locate the sign change of the normal force as $H/L$ increases.

What would settle it

Simulate simple shear of a cube with $\beta$ close to $-1$ (for example, $\beta=-0.9$ or the pure $I_2$ material with $C_1=0$) using the same finite-element setup and read the sign of the normal reaction; any positive value disproves the paper's universal cube claim. A laboratory version would be to shear a cube of an $I_2$-dominated rubber and measure whether it pushes the platens apart.

Watch

Extended reading notes

Core claim

The central claim is that the sign of the Poynting normal force in a sheared soft cuboid is controlled by the aspect ratio $H/L$, not just by the material. For thin blocks ($H/L=0.25$) the classical prediction of the homogeneous-shear theory is recovered, with the normal force proportional to $-(\mu/2)(1+\beta)K^2$ per unit area, where $\beta$ parameterizes the Mooney–Rivlin constants. For a cube ($H/L=1$) the computed and measured normal force is negative, which is the reverse Poynting effect. The paper maps the neutral curve of critical $H/L$ against $\beta$ where the force vanishes and concludes that every cube produces the reverse effect for all third-order incompressible isotropic solids, not only for special materials.

Load-bearing premise

The universal cube claim rests on finite-element simulations that scan only the range $\beta\in[-0.3,1.0]$ and on experiments at just two aspect ratios, so if a material near the other end of the Mooney–Rivlin range gave a positive normal force for a cube, the 'always' would fail.

Editorial extensions

If this is right

A standard thin-block shear test with $H/L\le 0.25$ stays in the classical positive-Poynting regime, so the usual test protocol is not invalidated by the reversal.
For any given soft material, a specific block height can be chosen so that the vertical normal force vanishes, which can eliminate unwanted vertical coupling in sheared bearings or isolators.
Cubic test specimens should be avoided when the goal is to measure the homogeneous Poynting response, because the cubic geometry itself produces the reverse effect.
The reversal is available to ordinary isotropic rubbers and silicones, so no fibers, porosity, compressibility, or strain stiffening is needed to achieve negative normal stress.

Reading between the lines

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

The neutral curve is computed only for $\beta\in[-0.3,1.0]$, and the 'cubes always' claim implicitly predicts that the curve stays below $H/L=1$ across the full range $[-1,1]$; an analytical boundary-layer solution could test this without relying on the finite-element scan.
The same geometric mechanism may apply to other finite geometries, such as prisms of different cross-sections or bonded layers in torsion, where a critical shape could likewise cancel the normal force; the paper does not test those cases.
Because the effect is quadratic in shear, the cancellation is exact only at one aspect ratio for a given material; a practical isolator would need the ratio tuned near the neutral curve and would still show residual second-order forces away from it.
An experimental check of the predicted critical ratio for the same silicone at intermediate $H/L$ would directly confirm the location of the neutral curve rather than only its two endpoints.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

First, the thing to know: this paper has a solid core—aspect-ratio-driven reversal of the Poynting effect in isotropic incompressible third-order solids—and an overstretched headline. The experiments show a clear sign change between a thin block (H/L=0.25) and a cube (H/L=1.0) for the same silicone. The FE critical curve for the cancellation ratio is plausible and consistent with the experimental reversal at the tested material parameter (β≈0.7). That is genuinely new: previous reversals needed fibres, compressibility, porosity, or stiffening; here geometry alone does it.

What's good: the experimental design is careful (n=8-9, small standard deviations), the FE uses standard hybrid elements for incompressible material and reports convergence, and the paper is honest about the current limitations of the setup. The practical message—that shear testing protocols using thin blocks may inadvertently suppress or cancel the Poynting effect if the aspect ratio is near the critical value—is useful.

Now the soft spots. The central claim that cubes always reverse the effect, irrespective of material parameters, is not supported by the evidence. The FE covers only β∈[-0.3,1], and no argument extends the curve to β<-0.3. The neo-Hookean endpoint β=-1 is the dangerous case: homogeneous theory gives zero normal force, so the finite-geometry correction decides the sign, and the paper doesn't compute or bound it. This is a load-bearing gap for the abstract's strongest sentence. The authors should either prove the claim or soften it to the tested range.

Second, the experimental normal forces are sub-Newton (about -0.1 to -0.2 N at the largest shear), yet they used a 500 N load cell with advertised accuracy <0.5%. If that's full-scale accuracy, the uncertainty is ±2.5 N—an order of magnitude above the measured signal. The consistency across eight samples suggests a real effect, but the load-cell specification needs to be clarified (is it % of reading? of full scale? what resolution?). Without that, the experimental sign reversal is suggestive, not definitive.

Third, the paper cites an asymptotic treatment [8] but doesn't use it to check how much of the reversal was already implicit there. A careful comparison would either strengthen the universal claim or reveal its limits.

Overall: the phenomenon is likely real, the central idea is worth pursuing, and the paper deserves a serious referee. But the universal cube statement should be revised downward or backed by analysis at low β, and the load-cell issue must be addressed. I would send it to review with expectation of major revision, and I'd want to see the revised version.

Referee Report

2 major / 5 minor

Summary. The paper studies the normal (Poynting) force generated when a soft incompressible cuboid is sheared between rigid platens. For thin samples the homogeneous simple-shear theory predicts a positive normal force; the authors show experimentally that a 20×20×5 mm silicone cuboid gives a positive normal force while a 10×10×10 mm cube gives a negative normal force. Using ABAQUS finite-element simulations with Mooney-Rivlin material parameters (µ=62.5 kPa, β∈[-0.3,1]), they compute the critical aspect ratio H/L at which the normal force vanishes as a function of β, and conclude that cubes always give a reverse Poynting effect for all incompressible isotropic third-order elastic solids.

Significance. If the universal cube claim holds, this is an appealing geometric route to cancel or reverse the Poynting effect, with potential relevance to soft-matter testing and seismic isolation. The paper has clear strengths: the critical curve is generated by direct FE computation rather than by fitting to the normal-force measurements, the material constants are identified from shear-force data, the FE mesh is refined with stated convergence checks, and the experiments provide a qualitative sign change that is consistent with the FE picture. The main weaknesses are that the universal claim rests on a partial parameter range and that the experimental normal forces are near the stated load-cell accuracy. These issues do not invalidate the observed reversal for the tested materials, but they leave the strongest claim in need of additional support.

major comments (2)

[Abstract, II (Results), III (Materials and Methods)] The universal statement that cubes always produce the reverse Poynting effect is not established by the presented evidence. The FE campaign varies β only from -0.3 to 1.0, leaving the neo-Hookean limit β=-1 and the interval [-1,-0.3) unexamined. Since the homogeneous theory predicts exactly zero normal force at β=-1, the sign for a cube in that limit is controlled entirely by the finite-geometry correction, which is neither computed nor bounded. A concrete remedy is to run the FE calculation at β=-1 and at least one intermediate value such as -0.5, and to report the sign of the normal force for H/L=1; if the sign remains negative throughout, the claim can be retained with a revised statement about the tested range.
[III (Materials and Methods), Fig. 1] The experimental normal-force measurements are at the margin of the stated load-cell accuracy. Normal forces in Fig. 1 are on the order of 0.1-0.2 N, while the 500 N load cell used for the normal force is quoted with accuracy <0.5%. If this figure is a percentage of full scale, the absolute uncertainty is about ±2.5 N, which exceeds the measured signals and makes the negative values in Fig. 1(b) indistinguishable from zero. The authors should report the calibration certificate, specify whether accuracy is relative to reading or full scale, and provide error bars on the normal-force data; otherwise the experimental sign change is not quantitatively supported.

minor comments (5)

[Abstract, II] The abstract and Section II state that cubes always reverse the Poynting effect; until the FE range is extended, these statements should be qualified as holding for β∈[-0.3,1.0] or supported by an additional argument.
[Fig. 1, II] In Figure 1 and the text, the terminology for the sample dimension H alternates between 'height' and 'thickness'; please choose one and label the axes consistently (e.g., H/L in the figure captions).
[II, III] The inverse FE identification of µ=62.5 kPa and β≈0.7 is mentioned as 'not shown' in Section II but never described; a short paragraph in Materials and Methods stating the objective function and the measured data used would make the material characterization reproducible.
[III (Materials and Methods)] The mesh refinement criterion 'minimum grid size equal or less than 0.02H' is stated, but the reader is not told how the reported normal force varies with mesh size; one convergence plot or table would substantiate the claim of convergence.
[IV (Conclusion), Ref. [19]] Reference [19] is used to illustrate unphysical model response with a cubic geometry; the specific finding being cited is not identified, so the relevance to the present reversal effect is unclear.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the critical aspect-ratio curve is a direct FE computation compared with independent experiments, not a fit to the predicted normal-force data.

full rationale

The paper's central derivation chain is self-contained. The classical homogeneous-shear result σ22 = -(µ/2)(1+β)K² is used only as background and is not the source of the reversal claim. The critical H/L curve in Figure 3 is generated by direct finite-element computation of the normal force for many aspect ratios and β values, and the sign change is read off the computed response rather than fitted to the experimental normal-force measurements. The experiments provide independent evidence at two aspect ratios (H/L = 0.25 and 1.0) for the silicone sample, and the FE curve is consistent with those observations. The inverse analysis used to identify µ and β is not shown in detail, but the paper does not indicate that the critical-curve shape was fitted to the normal-force data; the curve varies nontrivially with β and H/L, so the reversal prediction is not forced by construction. The only self-citations (e.g., [6] for the equivalence of Mooney-Rivlin and third-order elasticity, [12] for negative Poynting effects in fibrous tissues) are standard contextual references and are not load-bearing for the present geometric-reversal claim. The assertion that cubes 'always' reverse the Poynting effect for all β in [-1,1] is an extrapolation beyond the simulated range β in [-0.3,1], but that is a generality gap, not circularity: the FE model does not encode the cube result as an input, and the neo-Hookean endpoint β = -1 is simply untested. Therefore no step in the derivation reduces to its own inputs, and the circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim depends on two fitted material parameters (µ, β) used in FE, and on the modeling assumption that the Mooney-Rivlin third-order description and the ABAQUS boundary value problem faithfully represent the sheared cuboid. No new entities are introduced.

free parameters (2)

shear modulus µ_silicone = 62.5 kPa
Determined by inverse FE analysis of the silicone samples; used as input to FE simulations and to place experimental points in Figure 3.
Mooney-Rivlin parameter β_silicone = ≈0.7
Determined by inverse analysis from the shear response; used in FE simulations and to locate the experimental samples in the H/L versus β map.

assumptions (4)

domain assumption Third-order incompressible isotropic elasticity is equivalent to the Mooney-Rivlin form for small-but-finite shear
Invoked after Equation (2) to justify the use of Mooney-Rivlin constants for all solids at the level of approximation used.
domain assumption The silicone samples and simulated solids are perfectly incompressible, isotropic, homogeneous Mooney-Rivlin materials
Assumed in the FE model and in interpreting the experiments; slight compressibility is known to affect the Poynting effect.
domain assumption ABAQUS hybrid brick elements C3D8RH with the stated mesh sizes give a converged solution for the normal reaction force
Stated in Materials and Methods that convergence was checked for minimum grid size ≤0.02H, but no convergence data are shown.
domain assumption The normal reaction force at the top platen equals the Poynting normal force that would be felt in a shear test
The FE extracts the normal force by measuring the reaction on the top plate; edge effects near the corners are assumed not to affect the total force.

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Cite this review

Pith. "Pith review of Canceling the elastic Poynting effect with geometry." pith.science (2026). https://pith.science/paper/44PXFI6W

@misc{pith2026250603821,
  author       = {Pith},
  title        = {Pith review of: Canceling the elastic Poynting effect with geometry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/44PXFI6W}},
  note         = {Machine review of arXiv:2506.03821}
}

read the original abstract

The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using Finite Element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity).

Figures

Figures reproduced from arXiv: 2506.03821 by the authors.

**Figure 2.** illustrates our strategy when β = 0.3 and H/L varies between 0.47 and 0.53. We see that the computed normal force switches from a positive value (classical Poynting effect) to a negative value (reverse Poynting effect) as H/L increases, and is almost zero (canceled Poynting effect) when H/L = 0.495, giving one point in our H/L Vs β graph displayed on [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 1.** FIG. 1. Experimental shear of a soft block. (a) When the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 3.** FIG. 3. Plot of the critical aspect ratio [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [8]

Wang and M

D. Wang and M. Wu, Generalized shear of a soft rect- angular block, Journal of the Mechanics and Physics of Solids70, 297 (2014)

work page 2014

[2] [1]

J. H. Poynting, On pressure perpendicular to the shear planes in finite pure shears, and on the lengthening of loaded wires when twisted, Proceedings of the Royal So- ciety of London. Series A, Containing Papers of a Math- ematical and Physical Character82, 546 (1909)

work page 1909

[3] [2]

R. S. Rivlin, Torsion of a rubber cylinder, Journal of Applied Physics18, 444 (1947)

work page 1947

[4] [3]

R. S. Rivlin, Large elastic deformation of isotropic ma- terials iv. Further developments of the general theory, Philosophical Transactions of the Royal Society of Lon- donA241, 379 (1948)

work page 1948

[5] [4]

Balbi, A

V. Balbi, A. Trotta, M. Destrade, and A. N. Annaidh, Poynting effect of brain matter in torsion, Soft matter 15, 5147 (2019)

work page 2019

[6] [5]

R. S. Rivlin, Large elastic deformation of isotropic ma- terials vii. Experiments on the deformation of rubber, Philosophical Transactions of the Royal Society of Lon- donA243, 251 (1951)

work page 1951

[7] [6]

Destrade, M

M. Destrade, M. D. Gilchrist, and J. G. Murphy, Onset of nonlinearity in the elastic bending of blocks, Journal of Applied Mechanics77(2010)

work page 2010

[8] [7]

ISO 1827:2022,Rubber, vulcanized or thermoplastic – De- termination of shear modulus and adhesion to rigid plates – Quadruple-shear methods, Standard (International Or- ganization for Standardization, Geneva, CH, 2022)

work page 2022