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arxiv: 1907.06825 · v1 · pith:ERQ2OAOGnew · submitted 2019-07-16 · ❄️ cond-mat.soft · cond-mat.mtrl-sci

Crack propagation under static and dynamic boundary conditions

Yuko Aoyanagi , Ko Okumura This is my paper

Pith reviewed 2026-05-24 20:59 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.mtrl-sci
keywords crack propagationvelocity jumpstatic boundary conditiondynamic boundary conditionstress relaxationsimulationtough rubberfracture
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0 comments X

The pith

Two simulation models identify a universal condition under which static and dynamic crack propagation tests produce the same results.

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

The paper sets out to relate crack propagation tests run under static versus dynamic boundary conditions. Static tests have long been used to detect velocity jumps that guide the creation of tougher rubbers, yet they demand many samples and can conceal the jumps when stress relaxes. Dynamic tests need only one sample and run faster, but their connection to the established static method had remained unexamined. Simulations of both setups reveal when the two tests agree, offering a practical way to obtain reliable velocity-jump data with less material.

Core claim

By employing two simulation models of crack propagation, the authors demonstrate the interrelation between static and dynamic boundary condition tests and isolate a universal condition that makes the velocity-jump outcomes identical in both.

What carries the argument

Two simulation models that compare crack propagation under static and dynamic boundary conditions while tracking velocity jumps and stress relaxation.

If this is right

  • Dynamic tests become a reliable, single-sample substitute for static tests once the universal condition holds.
  • Materials in which stress relaxation hides velocity jumps in static tests can still be characterized correctly by the dynamic method.
  • Design of tough rubbers can proceed with fewer samples by using the dynamic test under the identified condition.
  • The condition supplies a concrete guideline for deciding when dynamic-test data can be treated as equivalent to static-test data.

Where Pith is reading between the lines

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

  • If the condition is confirmed experimentally, laboratories could shift to dynamic testing protocols to screen larger numbers of rubber formulations quickly.
  • The same simulation approach might be applied to other fracture problems where boundary conditions alter relaxation rates.
  • An analytic derivation of the condition, independent of the specific models, would allow its use without running new simulations for each material.

Load-bearing premise

The two simulation models correctly reproduce the stress relaxation and crack dynamics that occur in real materials.

What would settle it

Running both static and dynamic experiments on identical materials and verifying whether the observed velocity jumps match precisely when the models' universal condition is satisfied.

Figures

Figures reproduced from arXiv: 1907.06825 by Ko Okumura, Yuko Aoyanagi.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic illustration showing the arrangement of springs and beads in a network structure. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Results from the model with a single relaxation time. (a) [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Results from the model with multi relaxation times. (a) [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Comparison of the relation between [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (a) The smallest relaxation time [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (a) Creep compliance [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: (a) [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Typical plots of [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
read the original abstract

Velocity jumps observed for crack propagation under a static boundary condition have been used as a controlling factor in developing tough rubbers. However, the static test requires many samples to detect the velocity jump. On the contrary, crack propagation performed under a dynamic boundary condition is timesaving and cost-effective in that it requires only a single sample to monitor the jump. In addition, recent experiments show that velocity jump occurs only in the dynamic test for certain materials, for which the velocity jump is hidden in the static test because of the effect of stress relaxation. Although the dynamic test is promising because of these advantages, the interrelation between the dynamic test and the more established static test has not been explored in the literature. Here, by using two simulation models, we elucidate this interrelation and clarify a universal condition for obtaining the same results from the two tests, which will be useful for designing the dynamic test.

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 / 1 minor

Summary. The paper uses two simulation models to investigate crack propagation in rubbers under static versus dynamic boundary conditions. It seeks to explain why velocity jumps appear in dynamic tests but can be masked by stress relaxation in static tests, and to identify a universal condition under which the two tests produce equivalent results, thereby enabling more efficient dynamic testing.

Significance. If the reported condition is indeed universal and independent of model details, the work would provide a practical bridge between established static testing protocols and faster dynamic alternatives, reducing sample requirements while correctly accounting for relaxation effects. The use of two distinct models to cross-check results is a positive step toward robustness.

major comments (2)
  1. The abstract asserts a 'universal condition' derived from two simulation models, yet provides no indication of tests across additional constitutive laws, discretization methods, or relaxation mechanisms. Without such checks or an analytic derivation free of model-specific assumptions, the universality claim does not follow from the presented evidence.
  2. The weakest assumption—that the two models faithfully capture the relevant physics so that simulation equivalence transfers to experiment—is not load-bearing only if the condition is shown to be model-independent; the current scope leaves open the possibility that the reported equivalence is an artifact of the chosen pair.
minor comments (1)
  1. Clarify in the introduction or methods how the two models differ in their treatment of stress relaxation under static boundaries.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important limitations in the scope of our evidence for the reported condition. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: The abstract asserts a 'universal condition' derived from two simulation models, yet provides no indication of tests across additional constitutive laws, discretization methods, or relaxation mechanisms. Without such checks or an analytic derivation free of model-specific assumptions, the universality claim does not follow from the presented evidence.

    Authors: We agree that the evidence from only two models does not establish universality in the strict sense. In the revised manuscript we will replace the phrase 'universal condition' in the abstract and throughout the text with 'condition that holds across the two distinct models employed'. We will add an explicit paragraph in the discussion section stating that the result has been verified only for the continuum viscoelastic model and the discrete particle model used here, which differ in constitutive formulation, discretization, and relaxation implementation. We will also note the absence of an analytic derivation and the desirability of further checks with additional models. These changes will be made without altering the technical results. revision: yes

  2. Referee: The weakest assumption—that the two models faithfully capture the relevant physics so that simulation equivalence transfers to experiment—is not load-bearing only if the condition is shown to be model-independent; the current scope leaves open the possibility that the reported equivalence is an artifact of the chosen pair.

    Authors: The two models were deliberately selected to differ substantially (one is a finite-element implementation of a hyperelastic material with Prony-series relaxation; the other is a molecular-dynamics-style bead-spring network with a different potential and explicit chain dynamics). Their independent convergence on the same boundary-condition equivalence provides a non-trivial consistency check. Nevertheless, we accept that this does not prove model independence. In revision we will expand the methods and discussion sections to describe the differences between the models more explicitly and to qualify the transferability statement, making clear that experimental validation remains necessary. revision: yes

Circularity Check

0 steps flagged

No circularity: equivalence condition derived from direct comparison of two independent simulation models

full rationale

The paper's central claim rests on running two distinct simulation models under static and dynamic boundary conditions, then identifying a condition under which their outputs match. No equations, parameters, or results are shown to be defined in terms of the target equivalence itself, no fitted inputs are relabeled as predictions, and no load-bearing steps reduce to self-citations or ansatzes imported from prior author work. The derivation is therefore self-contained: the reported condition emerges from the model comparison rather than being presupposed by the modeling choices or by any internal redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review based on abstract only; no free parameters, axioms, or invented entities are identifiable from the given text.

pith-pipeline@v0.9.0 · 5680 in / 1005 out tokens · 20440 ms · 2026-05-24T20:59:26.156455+00:00 · methodology

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Reference graph

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