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Stochastic homogenization for a scalar viscoelastic model exhibiting stress–strain hysteresis
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Hudson, Thomas E. (Edward), Legoll, Frédéric and Lelièvre, Tony (2020) Stochastic homogenization for a scalar viscoelastic model exhibiting stress–strain hysteresis. ESAIM : M2AN, 54 (3). 879 - . doi:10.1051/m2an/2019081 ISSN 0764-583X.
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WRAP-stochastic-homogenization-scalar-viscoelastic-model-hysteresis-Hudson-2019.pdf - Accepted Version - Requires a PDF viewer. Download (1150Kb) | Preview |
Official URL: https://doi.org/10.1051/m2an/2019081
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.
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||
| Library of Congress Subject Headings (LCSH): | Stochastic analysis, Hysteresis, Homogenization (Differential equations) , Viscoelasticity | |||||||||||||||
| Journal or Publication Title: | ESAIM : M2AN | |||||||||||||||
| Publisher: | EDP Sciences | |||||||||||||||
| ISSN: | 0764-583X | |||||||||||||||
| Official Date: | May 2020 | |||||||||||||||
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| Volume: | 54 | |||||||||||||||
| Number: | 3 | |||||||||||||||
| Page Range: | 879 - | |||||||||||||||
| DOI: | 10.1051/m2an/2019081 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| Date of first compliant deposit: | 27 November 2019 | |||||||||||||||
| Date of first compliant Open Access: | 27 November 2019 | |||||||||||||||
| RIOXX Funder/Project Grant: |
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