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Motivated by rate-independent stress-strain hysteresis observed in filledrubber, this article considers a scalar viscoelastic model in which theconstitutive law is random and varies on a lengthscale which is small relativeto the overall size of the solid. Using stochastic two-scale convergence asintroduced by Bourgeat, Mikelic and Wright, we obtain the homogenized limit ofthe evolution, and demonstrate that under certain hypotheses, the homogenizedmodel exhibits hysteretic behaviour which persists under asymptotically slowloading. These results are illustrated by means of numerical simulations in aparticular one-dimensional instance of the model.

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