| Issue |
ESAIM: M2AN
Volume 54, Number 3, May-June 2020
|
|
|---|---|---|
| Page(s) | 879 - 928 | |
| DOI | https://doi.org/10.1051/m2an/2019081 | |
| Published online | 01 April 2020 | |
Stochastic homogenization of a scalar viscoelastic model exhibiting stress–strain hysteresis
1
CERMICS, École des Ponts ParisTech, 77455 Marne-La-Vallée Cedex 2, France
2
MATHERIALS Project-team Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France
3
Laboratoire Navier, École des Ponts ParisTech, 77455 Marne-La-Vallée Cedex 2, France
* Corresponding author: t.hudson.1@warwick.ac.uk
Received:
15
February
2018
Accepted:
19
November
2019
Motivated by rate-independent stress–strain hysteresis observed in filled rubber, this article considers a scalar viscoelastic model in which the constitutive law is random and varies on a lengthscale which is small relative to the overall size of the solid. Using a variant of stochastic two-scale convergence as introduced by Bourgeat et al., we obtain the homogenized limit of the evolution, and demonstrate that under certain hypotheses, the homogenized model exhibits hysteretic behaviour which persists under asymptotically slow loading. These results are illustrated by means of numerical simulations in a particular one-dimensional instance of the model.
Mathematics Subject Classification: 74Q10 / 35Q74
Key words: Hysteresis / stochastic homogenization / viscoelasticity / nonlinear time-dependent PDEs
© EDP Sciences, SMAI 2020
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