Resolving a controversy about adhesion in sliding contacts

G. Cricr\`i; M.Ciavarella

REVIEW 2 major objections 3 minor 19 references

Resolving a controversy about adhesion in sliding contacts

T0 review · 2 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A JKR adhesive contact under constant shear stress has an effective surface energy reduced by $\frac{3\sqrt{\pi}k_w}{4}\frac{\tau^2 a}{E^*}$, so tangential loading shrinks the contact area rather than enlarging it.

desk verdict The paper identifies a real controversy, but the central Legendre transform drops the -τ dW/dA term, flipping the sign of the shear correction and making the conclusion an artifact. read the letter →

arxiv 1908.04490 v1 pith:K5R3P523 submitted 2019-08-13 cond-mat.soft cond-mat.mtrl-sci

G. Cricrì , M.Ciavarella This is my paper · ORCID

classification cond-mat.softcond-mat.mtrl-sci

keywords adhesionJKRcontactslidingfrictioneffectivesurfaceenergymixed-modefractureareareductionshearstressthermodynamicpotential

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

This paper sets out to settle a dispute in the mechanics of adhesive sliding contacts: one recent thermodynamic model predicted that a constant tangential shear stress at the interface should enlarge the contact area, in conflict with classical fracture-mechanics theories and with experiments. The authors re-derive the equilibrium from energy minimization at fixed indentation and fixed shear stress, obtaining $G_{Ic,\mathrm{eff}} = G_{Ic} - \frac{3\sqrt{\pi}k_w}{4}\frac{\tau^2 a}{E^*}$. The correction is negative, so the contact area shrinks under shear, and a Legendre-transform calculation gives the same result. The paper concludes that the area-increase prediction is a paradox created by incomplete thermodynamics, that the classical reduction picture is quantitatively right, and that dissipative effects, not reversible shear adhesion, must be invoked to explain the weaker reduction seen in experiments.

What carries the argument

The central object is the effective surface energy $G_{Ic,\mathrm{eff}}$ and the identity that carries the argument is the derivative of the shear strain energy with respect to area, $$\left(\frac{\partial U_E^T}{\partial A}\right)_{\delta,\tau} = \frac34\tau w = \frac{3\sqrt{\pi}k_w}{4}\frac{\$tau^{2}$ a}{E^*}.$$ This converts the mixed-mode sliding problem into an equivalent pure mode-I JKR problem with a renormalised surface energy. A Legendre transform $\psi=U-P\delta-W\tau$ provides a single free energy whose stationarity with respect to $\delta$, $\tau$, and $A$ returns the same equilibrium condition.

What would settle it

Recompute $\partial\psi/\partial A$ in the Legendre transform while keeping the term $-\tau\,\partial W/\partial A$ that appears when differentiating $\psi=U-P\delta-W\tau$ at fixed $\tau$; if that term is nonzero, the sign of the shear correction changes. A sliding-contact experiment on a soft incompressible elastomer that shows contact area increasing with imposed $\tau$ would also refute the paper's central claim.

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Extended reading notes

Core claim

The paper claims that for a JKR adhesive contact under a constant interfacial shear traction $\tau$, the equilibrium is governed by a reduced effective surface energy $$G_{Ic,\mathrm{eff}} = G_{Ic} - \frac{3\sqrt{\pi}\,k_w}{4}\frac{\$tau^{2}$ a}{E^*}, \qquad a=\sqrt{A/\pi},$$ rather than by the enhanced adhesion that a recent model inferred from the same assumptions. The derivation separates the elastic energy into normal and tangential parts, $U_E^N$ and $U_E^T=\frac12\tau W$ with $W=A\,w$, $w=k_w\tau A^{1/2}/E^*$, and minimizes $U=U_E^N+U_E^T-G_{Ic}A$ at fixed indentation and fixed $\tau$. The same condition is recovered from a Legendre-transformed free energy. Because the shear term is negative, the contact radius shrinks with tangential load, and the shrinkage is slightly stronger than the classical ideal-brittle result; at a critical size adhesion is destroyed and the contact becomes Hertzian.

Load-bearing premise

The result stands on treating the shear stress as a fixed external constraint while minimizing internal energy over contact area; if the shear traction is instead a load whose work changes when the area changes, its contribution reverses sign.

Editorial extensions

If this is right

At fixed shear stress, the contact radius follows the JKR equation with $G_{Ic}$ replaced by the reduced effective surface energy, so increasing $\tau$ monotonically shrinks the contact.
Adhesion disappears completely for contact sizes larger than $a_0 = \frac{4}{3\sqrt{\pi}k_w}\frac{E^*G_{Ic}}{\tau^2}$, where the solution reverts to the Hertzian, adhesion-free contact.
Because the prefactor $k_w=8/\pi^{3/2}$ makes the reduction slightly stronger than the ideal-brittle mixed-mode result, the model requires dissipative corrections to match the weaker area reduction observed in experiments.
The Legendre-transform free energy gives a single potential whose minimization yields both equilibrium load-displacement and equilibrium area conditions, so the method extends JKR-style thermodynamics to sliding contacts with prescribed shear stress.

Reading between the lines

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

Applied asperity by asperity, the size-dependent shear penalty predicts that larger adhesive micro-contacts are preferentially destroyed during sliding, giving a characteristic upper cutoff in the distribution of real contact area.
A companion calculation at fixed tangential displacement rather than fixed shear stress would clarify whether reported differences between load-controlled and displacement-controlled sliding experiments are thermodynamic or dissipative in origin.
The same splitting of normal and shear strain energies could be carried into randomly rough contact models, where it would predict shear-induced loss of adhesion that is missed by stress-based failure criteria alone.

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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

Dear colleague,

This short comment takes on a genuine controversy: Menga-Carbone-Dini predict that uniform tangential shear increases adhesive contact area, which contradicts experiments and all classical models. The authors are right to question that, and the paper is clearly written. But the central derivation is wrong, and the error is not cosmetic.

The problem shows up in Section 4. They define the Legendre potential ψ = U - P_eq δ - W_eq τ, then differentiate at fixed δ and τ. The term -W τ must contribute -τ dW/dA when A changes. Eq. (24) forgets that and keeps only -W dτ/dA, which is zero. Including the missing term reverses the sign of the shear contribution. The correct stationarity condition gives G_Ic,eff = G_Ic + (3√π k_w/4) τ²a/E*, the exact opposite of Eq. (18). The same mistake infects Section 3: when τ is controlled, the relevant free energy is U - τW, not U, and the extra -τ dW/dA flips the argument. So the paper's conclusion—shear reduces adhesion—is an artifact of a dropped term.

What is genuinely new here is almost nothing. The authors themselves say their result 'exactly corresponds to Savkoor and Briggs' and is 'completely in line with existing theories.' The only free parameter, k_w, is borrowed from MCD rather than derived. The paper does a clear job of summarizing the controversy and the relevant experiments, and the self-citations are not inappropriate in that context. But a correct thermodynamic treatment actually reproduces MCD's direction, which would strengthen the paradox rather than resolve it.

Bottom line: this is a teachable example of a Legendre-transform pitfall, and the writing is honest. But the load-bearing math is wrong, so the paper does not contribute a valid result. I would not bring it to the reading group for its content, though it could serve as a cautionary exercise. For this version, reject; if the authors fix the sign, a short corrected comment might be worth consideration.

Referee Report

2 major / 3 minor

Summary. The manuscript addresses the claim by Menga, Carbone and Dini (MCD) that a uniform tangential shear stress in a sliding adhesive contact increases the contact area. The authors perform a thermodynamic energy-minimization treatment for a JKR adhesive contact under constant shear stress and claim that the effective surface energy is reduced by a term proportional to tau^2 a/E*, giving an even stronger area reduction than Savkoor and Briggs. Two derivations are presented: a direct minimization of the total energy at fixed delta and tau (Section 3) and a Legendre-transform potential (Section 4). The paper concludes that the MCD paradox is resolved in favor of the classical area-reduction theories, with the caveat that dissipative adjustments are needed to match experiments.

Significance. If correct, the paper would resolve a genuine controversy in soft-contact mechanics and reconcile MCD with classical mixed-mode fracture results. Its strengths are that it treats a sharply posed problem, uses a transparent closed-form derivation with no fitted parameters (the coefficient k_w is taken from MCD), and explicitly acknowledges the experimental tension. However, the central derivation contains a sign error in the treatment of the prescribed shear stress: the work of the shear loading is dropped when differentiating the thermodynamic potential. Restoring the missing term reverses the sign of the shear correction to the effective surface energy, so the corrected calculation predicts an area increase rather than a decrease. The claimed resolution of the MCD paradox is therefore not supported.

major comments (2)

[Section 4, Eqs. (21), (24), (25)] The derivative of the Legendre potential in Eq. (21) is computed incorrectly. Since psi contains the term -W^{eq} tau, the derivative with respect to A at fixed delta and tau includes -tau dW^{eq}/dA. This term is absent from Eq. (24). With W^{eq}=k_w tau A^{3/2}/E*, one has dW^{eq}/dA=(3 sqrt(pi) k_w/2) tau a/E*. Setting the corrected derivative to zero gives dU_N/dA = G_Ic + (3 sqrt(pi) k_w/4) tau^2 a/E*, which is Eq. (18) with the opposite sign of the shear contribution. Thus Eq. (18) is not a consequence of the Legendre-transform calculation. Additionally, the presence of -P^{eq}delta in Eq. (21) is inconsistent with the stated control at fixed delta, since a Legendre transform of the normal degree of freedom would replace delta by P as the independent variable; at fixed delta this term should not appear.
[Section 3, Eq. (17)] The direct minimization in Section 3 has the same defect. For a prescribed shear traction tau, the appropriate potential whose minimum defines equilibrium is U - tau W, not U, because the loading agency does work tau dW when the contact area changes at fixed tau. Equation (17) omits this work term. Restoring it changes the stationarity condition to dU_N/dA = G_Ic + (3 sqrt(pi) k_w/4) tau^2 a/E*, again reversing the sign of the shear correction in Eq. (18). Since the paper's central claim is the area-reduction sign of this term, the error is load-bearing and not a local typographical issue.

minor comments (3)

[Abstract and Conclusion] There are typographical errors such as 'adjustements' instead of 'adjustments', and some missing spaces and punctuation in the first paragraph of Section 1; these should be corrected.
[Footnote to Eq. (3)] The footnote for force control writes G = (partial U_E / partial A)_{S,delta} = (partial U_E/partial A + partial U_P/partial A)_P = G_Ic, but the first derivative is taken at fixed S,delta while the following expression is at fixed P. Please clarify the intended fixed-load expression.
[Section 3, after Eq. (18)] The comparison with Savkoor and Briggs relies on the sign of the shear term in Eq. (18); with the corrected sign the claim that the present model gives an even stronger reduction than Savkoor and Briggs no longer follows and should be revised.

Circularity Check

0 steps flagged · score 1.0 of 10

No circularity found: Eq. 18 is an independent energy-minimization result, and the self-citations are not load-bearing.

full rationale

The derivation chain is self-contained in the sense required by the circularity rubric: the central result, Eq. 18, is obtained by differentiating an explicitly stated strain-energy expression U_T = (1/2) tau W with W = k_w tau A^(3/2)/E* (Section 3), and it is not fitted to the target conclusion, nor does it rename a known result. The coefficient k_w is taken from MCD, but it is an input parameter, not a fitted output, and the prediction of reduced effective surface energy is a logically independent consequence of the stated energy balance. The Legendre-transform procedure in Section 4 is algebraically defective: Eq. 24 omits the -tau dW/dA term that arises when differentiating psi = U_N + U_T - G_Ic A - P delta - W tau with respect to A at fixed delta and tau. Restoring that term flips the sign of the shear correction and reverses the main conclusion, but this is a derivation error, not a circular reduction of the conclusion to its inputs. The self-references by the authors (e.g. [9], [10], [12], [13]) support the empirical context of contact-area reduction under shear and are not premises of the thermodynamic calculation; therefore they do not make the argument circular. No circular step can be quoted or exhibited, so the score is low, reflecting only the non-load-bearing presence of some author self-citations.

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

No fitted parameters appear; the inputs are material constants and the elastic coefficient k_w. The central burden is the choice of thermodynamic potential under constant shear traction, which the paper handles incorrectly by omitting the tau dW/dA term in the Legendre transform.

assumptions (5)

domain assumption JKR delta-function adhesion and large Tabor parameter are assumed.
Section 2, Eq. 4 sets the JKR limit as the framework for the whole calculation.
domain assumption Normal and tangential elastic fields decouple because the material is incompressible (Poisson ratio 0.5) or Dundurs' second constant is zero.
Section 3 after Eq. 10 splits U_E into U_N and U_T, which requires this decoupling.
domain assumption The shear traction is uniform and constant, with strain energy U_T = (1/2) tau W and W = k_w tau A^(3/2) / E*.
Section 3, Eqs. 13-15 adopt this constitutive and loading model from MCD and the elastic solution.
domain assumption The process is reversible and isentropic, with no dissipative effects.
Section 3 states the authors 'neglect variations of entropy' and treat the transformation as purely reversible, matching the 'ideally brittle' limit.
ad hoc to paper At fixed shear stress tau, equilibrium is obtained by minimizing U without including the external load potential -tau W.
This is the load-bearing premise and the source of the sign error. For traction-controlled loading the correct potential is U - tau W, and Eq. 24 omits the -tau dW/dA term.

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Cite this review

Pith. "Pith review of Resolving a controversy about adhesion in sliding contacts." pith.science (2026). https://pith.science/paper/K5R3P523

@misc{pith2026190804490,
  author       = {Pith},
  title        = {Pith review of: Resolving a controversy about adhesion in sliding contacts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K5R3P523}},
  note         = {Machine review of arXiv:1908.04490}
}

read the original abstract

An interesting recent paper by Menga, Carbone & Dini (MCD, 2018, [1]), suggests that in sliding adhesive contacts, the contact area should increase due to tangential shear stresses at the interface, assumed to be constant and corresponding to a material constant. This is not observed in the known experiments, and is in sharp contrast with all the classical theories about the transition from stick to sliding, both in the JKR (Griffith like) conditions which involve singular pressure and shear, as well as in full general cohesive models. We offer a rigorous thermodynamics calculation, which suggests in fact there is no qualitative contrast but a very close quantitative agreement, with previous theories. Actually, the model predicts an even stronger reduction of contact area than predicted by Savkoor and Briggs, contrary to experimental observations, so would certainly require some adjustements to consider dissipative effects.

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Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

19 extracted references · 18 canonical work pages

[1]

Menga, N., Carbone, G., & Dini, D. (2018). Do uniform tangential in terfacial stresses enhance adhesion?. Journal of the Mechanics and Phys ics of Solids, 112, 145-156. 7

work page 2018
[2]

Chateauminois, A., & Fretigny, C. (2008). Local friction at a slidin g interface between an elastomer and a rigid spherical probe. The Eu ropean Physical Journal E: Soft Matter and Biological Physics, 27(2), 22 1-227

work page 2008
[3]

G., & Hutchinson, J

Evans, A. G., & Hutchinson, J. W. (1989). Eﬀects of non-planar ity on the mixed mode fracture resistance of bimaterial interfaces. Act a Metallurgica, 37(3), 909-916

work page 1989
[4]

C., & Evans, A

Cao, H. C., & Evans, A. G. (1989). An experimental study of the fracture resistance of bimaterial interfaces. Mechanics of materials, 7(4) , 295-304

work page 1989
[5]

Hutchinson, J. W. (1990). Mixed mode fracture mechanics of int erfaces. Metal-ceramic interfaces, 295-306

work page 1990
[6]

Savkoor, A. R. & Briggs, G. A. D. (1977), The eﬀect of a tangen tial force on the contact of elastic solids in adhesion. Proc. R. Soc. Lon d. A 356, 103–114

work page 1977
[7]

L., (1997), Adhesion and friction between a smooth elastic spherical asperity and a plane surface

Johnson, K. L., (1997), Adhesion and friction between a smooth elastic spherical asperity and a plane surface. In Proceedings of the Roy al Society of London A453, No. 1956, pp. 163-179)

work page 1997
[8]

Pallares, G

Sahli, R. Pallares, G. , Ducottet, C., Ben Ali, I. E. , Akhrass, S. Al , Guibert, M. , Scheibert J. , (2018) Evolution of real contact are a under shear, Proceedings of the National Academy of Sciences, 115 (3) 471-476; DOI: 10.1073/pnas.1706434115

doi:10.1073/pnas.1706434115 2018

Show all 19 references

[9]

Ciavarella, M. (2018). Fracture mechanics simple calculations to e xplain small reduction of the real contact area under shear. Facta univ ersitatis, series: mechanical engineering, 16(1), 87-91

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[10]

Papangelo, A., & Ciavarella, M. (2019). On mixed-mode fracture me- chanics models for contact area reduction under shear load in soft materials. Journal of the Mechanics and Physics of Solids, 124, 159-171

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Proc R Soc A 466:1303–1325

Waters JF, Guduru PR, (2009), Mode-mixity-dependent adhe sive con- tact of a sphere on a plane surface. Proc R Soc A 466:1303–1325

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[12]

Sahli, R., Pallares, G., Papangelo, A., Ciavarella, M., Ducottet, C., P on- thus, N., & Scheibert, J. (2019). Shear-induced anisotropy in rou gh elastomer contact. Physical Review Letters, 122(21), 214301

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Papangelo, A., Scheibert, J., Sahli, R., Pallares, G., & Ciavarella, M. (2019). Shear-induced contact area anisotropy explained by a fr acture mechan- ics model. Physical Review E, 99(5), 053005

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[14]

Maugis, D. (2013). Contact, adhesion and rupture of elastic s olids (Vol. 130). Springer Science & Business Media

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[15]

E∗ = ( 1− ν 2 1 E1 + 1− ν 2 2 E2 ) − 1 and Ei, νi are the Young modulus and Poisson ratio of the material couple

fundamental contribution, which introduced Griﬃth-like energ y balance in 1Under force control, instead, we easily get an alternative G = ( ∂U E ∂A ) S,δ = ( ∂U E ∂A + ∂U P ∂A ) P = GIc (3) 2 the world of contact mechanics, and was later discussed to be the c orrect limit for ...
[16]

L., Kendall, K

Johnson, K. L., Kendall, K. & Roberts, A. D. (1971) Surface en ergy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301–313

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[17]

(1977) Surface forces and surface interactions

Tabor, D. (1977) Surface forces and surface interactions. J. Colloid Interface Sci. 58, 2

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Barber, JR. (2018). Contact Mechanics. Springer, New York . 8

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Carpick, R. W., Agrait, N., Ogletree, D. F. & Salmeron, M. (1996) Variation of the interfacial shear strength and adhesion of a nano meter sized contact. Langmuir 12, 3334–3340. 9

1996

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Menga, N., Carbone, G., & Dini, D. (2018). Do uniform tangential in terfacial stresses enhance adhesion?. Journal of the Mechanics and Phys ics of Solids, 112, 145-156. 7

work page 2018

[2] [2]

Chateauminois, A., & Fretigny, C. (2008). Local friction at a slidin g interface between an elastomer and a rigid spherical probe. The Eu ropean Physical Journal E: Soft Matter and Biological Physics, 27(2), 22 1-227

work page 2008

[3] [3]

G., & Hutchinson, J

Evans, A. G., & Hutchinson, J. W. (1989). Eﬀects of non-planar ity on the mixed mode fracture resistance of bimaterial interfaces. Act a Metallurgica, 37(3), 909-916

work page 1989

[4] [4]

C., & Evans, A

Cao, H. C., & Evans, A. G. (1989). An experimental study of the fracture resistance of bimaterial interfaces. Mechanics of materials, 7(4) , 295-304

work page 1989

[5] [5]

Hutchinson, J. W. (1990). Mixed mode fracture mechanics of int erfaces. Metal-ceramic interfaces, 295-306

work page 1990

[6] [6]

Savkoor, A. R. & Briggs, G. A. D. (1977), The eﬀect of a tangen tial force on the contact of elastic solids in adhesion. Proc. R. Soc. Lon d. A 356, 103–114

work page 1977

[7] [7]

L., (1997), Adhesion and friction between a smooth elastic spherical asperity and a plane surface

Johnson, K. L., (1997), Adhesion and friction between a smooth elastic spherical asperity and a plane surface. In Proceedings of the Roy al Society of London A453, No. 1956, pp. 163-179)

work page 1997

[8] [8]

Pallares, G

Sahli, R. Pallares, G. , Ducottet, C., Ben Ali, I. E. , Akhrass, S. Al , Guibert, M. , Scheibert J. , (2018) Evolution of real contact are a under shear, Proceedings of the National Academy of Sciences, 115 (3) 471-476; DOI: 10.1073/pnas.1706434115

doi:10.1073/pnas.1706434115 2018