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

@article{Hudson2018StochasticHO,
  title={Stochastic homogenization of a scalar viscoelastic model exhibiting stress–strain hysteresis},
  author={Thomas Hudson and Fr{\'e}d{\'e}ric Legoll and Tony Leli{\`e}vre},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
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… Expand
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