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Homogenization for rate‐independent systems
Author(s) -
Timofte Aida,
Mielke Alexander
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610237
Subject(s) - homogenization (climate) , nonlinear system , mathematics , rate of convergence , mathematical analysis , statistical physics , physics , computer science , biodiversity , ecology , computer network , channel (broadcasting) , quantum mechanics , biology
This paper is devoted to the homogenization for a class of rate‐independent systems described by the energetic formulation . The associated nonlinear partial differential system has periodically oscillating coefficients, but has the form of a standard evolutionary variational inequality. Thus, the model applies to standard linearized elastoplasticity with hardening. Using the recently developed methods of two‐scale convergence , periodic unfolding and the new introduced one, periodic folding , we show that the homogenized problem can be represented as a two‐scale limit which is again an energetic formulation, but now involving the macroscopic variable in the physical domain as well as the microscopic variable in the periodicity cell. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)