Some examples of nonlinear homogenization involving nearly degenerate energies

K. Bhattacharya, R. V. Kohn, S. Kozlov

Research output: Contribution to journalArticlepeer-review

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
DOIs
StatePublished - 1999

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Fingerprint Dive into the research topics of 'Some examples of nonlinear homogenization involving nearly degenerate energies'. Together they form a unique fingerprint.

Cite this