Infinite-order laminates in a model in crystal plasticity

被引：11

作者：

Albin, Nathan ^{[1
]}

Conti, Sergio ^{[2
]}

Dolzmann, Georg ^{[3
]}

机构：

[1] CALTECH, Pasadena, CA 91101 USA

[2] Univ Duisburg Essen, Fachbereich Math, D-47057 Duisburg, Germany

[3] Univ Regensburg, NWF Math 1, D-93040 Regensburg, Germany

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2009年 / 139卷

基金：

美国国家科学基金会;

关键词：

OPTIMAL-DESIGN; ENERGY MINIMIZATION; RELAXATION; MICROSTRUCTURES; REGULARITY; CONJECTURE; INTEGRANDS; ENVELOPE;

D O I：

10.1017/S0308210508000127

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a geometrically nonlinear model for crystal plasticity in two dimensions, with two active slip systems and rigid elasticity. We prove that the rank-1 convex envelope of the condensed energy density is obtained by infinite-order laminates, and express it explicitly via the F-2(1) hypergeometric function. We also determine the polyconvex envelope, leading to upper and lower bounds to the quasiconvex envelope. The two bounds differ by less than 2%.

引用

页码：685 / 708

页数：24

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