Elastic energy minimization and the recoverable strains of polycrystalline shape-memory materials

Kaushik Bhattacharya, Robert V. Kohn

Research output: Contribution to journalArticle

Abstract

Shape-memory behavior is the ability of certain materials to recover, on heating, apparently plastic deformation sustained below a critical temperature. Some materials have good shape-memory behavior as single crystals but little or none as polycrystals, while others have good shape-memory behavior even as polycrystals. We propose a method for explaining the difference. Our approach is based on elastic energy minimization. It leads to a special class of nonlinear homogenization problems, involving integrands that are degenerate near the origin. We explore the behavior of these problems through various examples and bounds. The elementary "Taylor bound" and the newer "translation method" are central to our analysis.

Original languageEnglish (US)
Pages (from-to)99-180
Number of pages82
JournalArchive for Rational Mechanics and Analysis
Volume139
Issue number2
DOIs
StatePublished - Oct 21 1997

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ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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