Stochastic homogenization of a scalar viscoelastic model exhibiting stress-strain hysteresis

Abstract : 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 stochastic two-scale convergence as introduced by Bourgeat, Mikelic and Wright, 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.
Type de document :
Pré-publication, Document de travail
35 pages, 4 figures. 2018
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https://hal.archives-ouvertes.fr/hal-01710772
Contributeur : Tony Lelievre <>
Soumis le : vendredi 16 février 2018 - 12:25:44
Dernière modification le : jeudi 26 avril 2018 - 10:27:56

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  • HAL Id : hal-01710772, version 1
  • ARXIV : 1802.05549

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Thomas Hudson, Frédéric Legoll, Tony Lelièvre. Stochastic homogenization of a scalar viscoelastic model exhibiting stress-strain hysteresis. 35 pages, 4 figures. 2018. 〈hal-01710772〉

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