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Non‐periodic homogenization of infinitesimal strain plasticity equations
Author(s) -
Heida Martin,
Schweizer Ben
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400112
Subject(s) - infinitesimal , homogenization (climate) , plasticity , mathematics , mathematical analysis , evolution equation , operator (biology) , physics , biodiversity , ecology , biochemistry , chemistry , repressor , gene , transcription factor , biology , thermodynamics
We consider the Prandtl‐Reuss model of plasticity with kinematic hardening, aiming at a homogenization result. For a sequence of coefficient fields and corresponding solutions u ɛ , we ask whether we can characterize weak limits u whenu ɛ ⇀ u as ɛ → 0 . We assume neither periodicity nor stochasticity for the coefficients, but we demand an abstract averaging property of the homogeneous system on reference volumes. Our conclusion is an effective equation on general domains with general right hand sides. The effective equation uses a causal evolution operator Σ that maps strains to stresses; more precisely, in each spatial point x , given the evolution of the strain in the point x , the operator Σ provides the evolution of the stress in x .