Examples of nonlinear homogenization in plane strain involving degenerate energies

Isaac Chenchiah and Kaushik Bhattacharya

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Submission date: 03. Aug. 2004
Pages: 22
published in: Proceedings of the Royal Society of London / A, 461 (2005) 2063, p. 3681-3703 
DOI number (of the published article): 10.1098/rspa.2005.1515
Bibtex
with the following different title: Examples of nonlinear homogenization involving degenerate energies. I. Plane strain
Keywords and phrases: homogenization, shape-memory polycrystals, rigid-perfect plasticity, localization, checkerboard microstructure
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Abstract:
The study of polycrystals of shape-memory alloys and rigid-perfectly plastic materials gives rise to problems of nonlinear homogenization involving degenerate energies. This paper presents a characterization of the stress and strain fields in a class of problems in plane strain, and uses it to study examples including checkerboards and hexagonal microstructures. Consequences for shape-memory alloys and rigid-perfectly plastic materials are discussed.