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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
49/2004

Examples of nonlinear homogenization in plane strain involving degenerate energies

Isaac Chenchiah and Kaushik Bhattacharya

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.

Received:
03.08.04
Published:
03.08.04
Keywords:
homogenization, shape-memory polycrystals, rigid-perfect plasticity, localization, checkerboard microstructure

Related publications

inJournal
2005 Repository Open Access
Isaac Vikram Chenchiah and Kaushik Bhattacharya

Examples of nonlinear homogenization involving degenerate energies. I. Plane strain

In: Proceedings of the Royal Society of London / A, 461 (2005) 2063, pp. 3681-3703