Some examples of nonlinear homogenization involving nearly degenerate energies

被引：5

作者：

Bhattacharya, K ^{[1
]}

Kohn, RV

Kozlov, S

机构：

[1] CALTECH, Div Engn & Appl Sci, Pasadena, CA 91125 USA

[2] NYU, Courant Inst, New York, NY 10012 USA

[3] Univ Marseille, Dept Math, Marseille, France

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1999年 / 455卷 / 1982期

关键词：

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

D O I：

10.1098/rspa.1999.0324

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：567 / 583

页数：17

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