Some examples of nonlinear homogenization involving nearly degenerate energies

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

doi:10.1098/rspa.1999.0324

Some examples of nonlinear homogenization involving nearly degenerate energies

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

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	567-583
Number of pages	17
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	455
Issue number	1982
DOIs	https://doi.org/10.1098/rspa.1999.0324
State	Published - 1999

Keywords

checkerboard microstructure
homogenization
optimal bounds
shape-memory polycrystals

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rspa.1999.0324

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AU - Kohn, R. V.

AU - Kozlov, S.

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AB - 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.

KW - checkerboard microstructure

KW - homogenization

KW - optimal bounds

KW - shape-memory polycrystals

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JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 1982

ER -

Some examples of nonlinear homogenization involving nearly degenerate energies

Abstract

Keywords

ASJC Scopus subject areas

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