Some examples of nonlinear homogenization involving nearly degenerate energies

K. Bhattacharya, Robert Kohn, S. Kozlov

Research output: Contribution to journalArticle

Abstract

We consider a specific class of nonlinear homogenization problems. The microstructure is a sort of checkerboard polycrystal, and the energy of the basic crystal is degenerate in one direction. We give matching upper and lower bounds for the homogenized energy. The motivation for this problem lies in the recent work of Bhattacharya & Kohn on shape-memory polycrystals. Our results show that a bound proved therein is nearly sharp.

Original languageEnglish (US)
Pages (from-to)567-583
Number of pages17
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume455
Issue number1982
StatePublished - 1999

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Polycrystal
Polycrystals
polycrystals
homogenizing
Homogenization
Shape Memory
Energy
Shape memory effect
Sort
Microstructure
Upper and Lower Bounds
Crystal
Crystals
microstructure
energy
crystals
Class

Keywords

  • checkerboard microstructure
  • homogenization
  • optimal bounds
  • shape-memory polycrystals

ASJC Scopus subject areas

  • General

Cite this

Some examples of nonlinear homogenization involving nearly degenerate energies. / Bhattacharya, K.; Kohn, Robert; Kozlov, S.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 455, No. 1982, 1999, p. 567-583.

Research output: Contribution to journalArticle

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