2018/02/15 by Thomas Hudson, Hudson, Thomas, Frédéric Legoll +3
Computer Science · Engineering · #35Q74 #74Q10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Elasticity and Material Modeling #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1802.05549
openalex publication_date 2018/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Motivated by rate-independent stress-strain hysteresis observed in filled\nrubber, this article considers a scalar viscoelastic model in which the\nconstitutive law is random and varies on a lengthscale which is small relative\nto the overall size of the solid. Using stochastic two-scale convergence as\nintroduced by Bourgeat, Mikelic and Wright, we obtain the homogenized limit of\nthe evolution, and demonstrate that under certain hypotheses, the homogenized\nmodel exhibits hysteretic behaviour which persists under asymptotically slow\nloading. These results are illustrated by means of numerical simulations in a\nparticular one-dimensional instance of the model.\n