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
收藏
页码：685 / 708
页数：24
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