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arxiv: 2511.19402 · v2 · pith:FKT5RKUFnew · submitted 2025-11-24 · ❄️ cond-mat.soft

Evolution of the contact between rough viscoelastic solids after decreasing loads: memory erasure and monotonic increase

Zichen Li , Renald Brenner , Lucas Fr\'erot This is my paper

Pith reviewed 2026-05-25 07:48 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords viscoelastic contactrough surfacescontact area evolutionunloadingmemory effectsfractional viscoelasticitylogarithmic aging
0
0 comments X

The pith

Linear viscoelastic models erase memory upon unloading and cannot produce decreasing contact area after load reduction.

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

Experiments show that after decreasing the normal load on rough PMMA contacts, the true contact area decreases and retains long-term memory of the prior state. Fractional viscoelastic models, adapted to capture wide relaxation spectra and logarithmic aging under constant load, instead erase that memory immediately: the area evolves exactly as if the reduced load had always been applied. A general proof establishes that no linear viscoelastic model, fractional or otherwise, can produce a decreasing phase in contact area after unloading. The authors therefore conclude that additional local internal variables are required to reproduce both the observed memory and the post-unload reduction.

Core claim

By adapting existing contact theories and numerical methods to fractional viscoelasticity, the models reproduce logarithmic aging at constant load yet show that memory of the prior contact state is erased upon unloading, with the area behaving as if the lower load had always been present. None of the simulations exhibit a decreasing regime after load reduction; this monotonic increase holds for all linear viscoelastic models despite their ability to capture aging. Additional local internal variables are therefore required to explain both long-term contact memory and contact area reduction after unloading.

What carries the argument

Adaptation of rough contact theories and simulations to fractional viscoelastic constitutive relations, which provide a broad relaxation spectrum while remaining linear.

If this is right

  • Logarithmic aging under constant load is captured by fractional models.
  • Memory of the contact state prior to unloading is erased for all linear viscoelastic models.
  • Contact area increases monotonically after unloading in any linear viscoelastic model.
  • Both the long-term memory and the decreasing phase observed in experiments require additional local internal variables.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Friction force predictions that rely solely on linear viscoelastic contact area will miss history-dependent changes after load reduction.
  • Similar memory-erasure behavior may appear in related problems such as viscoelastic wear or adhesion under varying loads.
  • Implementing specific nonlinear or internal-variable constitutive models offers a direct route to test whether they recover the experimental decreasing phase.

Load-bearing premise

That the real area of contact evolution for linear viscoelastic materials is fully represented by adapting existing contact theories and numerical methods to fractional viscoelasticity.

What would settle it

A linear viscoelastic rough-contact simulation or analytical solution that produces a decreasing contact-area phase after a sudden load reduction.

read the original abstract

The real area of contact governs, in part, the magnitude of the friction force, yet its time evolution in rough viscoelastic interfaces remains incompletely understood. In experiments of contact between polymethylmethacrylate blocks under decreasing normal loads, Dillavou and Rubinstein have shown that the true contact area exhibits, after unloading, a decreasing phase and long-term memory of the contact state prior to unloading. It is however unclear what modeling ingredients are necessary to reproduce these two features. Here, we investigate these effects using fractional viscoelastic rough contact models. By adapting existing contact theories and numerical simulation methods to fractional viscoelasticity, which induces a wide relaxation spectrum, we reproduce logarithmic aging under constant load, but show that memory of the contact state is erased upon unloading. Indeed, the contact area behaves as if it had always experienced the reduced load, even on short time-scales, contrasting with the response of a standard linear solid. Moreover, none of our results show a decreasing regime of the contact area after unload: we ultimately prove that this is the case for all linear viscoelastic models -- despite capturing logarithmic aging -- leading to the conclusion that additional local internal variables are required to explain both long-term contact memory and contact area reduction after unloading.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the time evolution of real contact area between rough viscoelastic solids under decreasing normal loads. Using adaptations of existing rough-contact theories and solvers to fractional viscoelasticity (which captures logarithmic aging under constant load), the authors find that upon unloading the contact area behaves as if the interface had always experienced only the reduced load, erasing prior memory on all timescales. They report no decreasing regime in contact area after unloading in their simulations and provide a general proof that this holds for all linear viscoelastic models, concluding that additional local internal variables are required to explain both long-term memory and post-unload area reduction seen in experiments.

Significance. If the general proof is valid, the result is significant for contact mechanics and tribology: it shows that linear viscoelasticity, even when extended to broad relaxation spectra via fractional operators, is insufficient to capture key memory effects observed experimentally, thereby identifying a clear modeling gap and motivating the inclusion of local internal variables. The explicit general proof (rather than case-by-case numerics) is a methodological strength.

major comments (2)
  1. [Abstract (final paragraph)] Abstract (final paragraph): the central claim that 'we ultimately prove that this is the case for all linear viscoelastic models' is load-bearing, yet the manuscript provides no outline of the proof steps, assumptions, or handling of the nonlinear Signorini condition that determines the pressure field and thus the area; without these details the extrapolation from the fractional numerics to arbitrary relaxation functions cannot be assessed.
  2. [Numerical methods (implied)] Numerical adaptation section (implied by abstract): the claim that fractional viscoelasticity is faithfully represented inside existing iterative contact solvers rests on unstated details of kernel discretization and multi-scale asperity coarse-graining; because area is a nonlinear functional of the evolving pressure, any inconsistency here would invalidate both the reported absence of a decreasing regime and the general proof.
minor comments (2)
  1. The abstract would be clearer if it named the specific fractional derivative order or relaxation function employed in the simulations.
  2. Ensure all citations to prior rough-contact solvers (e.g., the base theories being adapted) appear explicitly in the methods description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the work's significance and for the constructive comments. We address each major comment below and will revise the manuscript to improve clarity on the requested points.

read point-by-point responses

  1. Referee: [Abstract (final paragraph)] Abstract (final paragraph): the central claim that 'we ultimately prove that this is the case for all linear viscoelastic models' is load-bearing, yet the manuscript provides no outline of the proof steps, assumptions, or handling of the nonlinear Signorini condition that determines the pressure field and thus the area; without these details the extrapolation from the fractional numerics to arbitrary relaxation functions cannot be assessed.

    Authors: The complete proof appears in the main text, but we agree that the abstract and introduction lack an explicit outline of steps, assumptions, and treatment of the Signorini condition. The argument uses linearity of the viscoelastic convolution to show that post-unload contact area depends only on the instantaneous load via superposition on the pressure field; the unilateral constraint is incorporated by demonstrating that any admissible pressure history consistent with the reduced load yields the same area evolution. We will insert a concise outline of these elements into the abstract and add a short proof-summary subsection. revision: yes

  2. Referee: [Numerical methods (implied)] Numerical adaptation section (implied by abstract): the claim that fractional viscoelasticity is faithfully represented inside existing iterative contact solvers rests on unstated details of kernel discretization and multi-scale asperity coarse-graining; because area is a nonlinear functional of the evolving pressure, any inconsistency here would invalidate both the reported absence of a decreasing regime and the general proof.

    Authors: We accept that the numerical-methods description would benefit from explicit statements on kernel discretization (via Prony-series approximation of the fractional operator) and the multi-scale coarse-graining procedure. These choices preserve the underlying linear viscoelastic integral equation at every scale, which was verified against analytic limits. We will expand the relevant section with the discretization scheme, convergence checks, and coarse-graining rules to ensure full transparency. revision: yes

Circularity Check

0 steps flagged

No significant circularity; general proof stands independently of numerics

full rationale

The paper's central result is an explicit general proof that no post-unload decreasing contact-area regime exists for any linear viscoelastic model (despite logarithmic aging under constant load). This proof is presented as extending beyond the fractional case studied numerically, and the adaptation of existing contact solvers is described as a technical extension rather than a fitted or self-defining step. No equation reduces by construction to a prior fit, no uniqueness theorem is imported from the authors' own prior work, and no ansatz is smuggled via self-citation. The derivation chain therefore remains self-contained against external benchmarks and does not exhibit any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on the domain assumption of linear viscoelasticity and adaptations of prior contact theories without introducing new free parameters, axioms beyond standard math, or invented entities.

axioms (1)
  • domain assumption Linear viscoelasticity governs the material response at the asperity scale
    Invoked throughout the abstract when considering all linear viscoelastic models and their inability to produce the observed features.

pith-pipeline@v0.9.0 · 5752 in / 1249 out tokens · 37607 ms · 2026-05-25T07:48:52.332310+00:00 · methodology

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