Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity

被引：9

作者：

Ghiba, Ionel-Dumitrel ^{[1
,2
,3
]}

Martin, Robert J. ^{[1
]}

Neff, Patrizio ^{[1
]}

机构：

[1] Univ Duisburg Essen, Lehrstuhl Nichtlineare Anal & Modellierung, Fak Math, Thea Leymann Str 9, D-45127 Essen, Germany

[2] Alexandru Ioan Cuza Univ, Dept Math, Blvd Carol 1,11, Iasi 700506, Romania

[3] Romanian Acad, Iasi Branch, Octav Mayer Inst Math, Iasi 700505, Romania

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2018年 / 116卷

关键词：

Rank-one convexity; Polyconvexity; Quasiconvexity; Nonlinear elasticity; Morrey's conjecture; Volumetric-isochoric split; SUFFICIENT CONDITIONS; STRONG ELLIPTICITY; EQUILIBRIUM EQUATIONS; QUADRATIC-FORMS; DIMENSIONS; STRAIN; QUASICONVEXITY; ELASTOSTATICS;

D O I：

10.1016/j.matpur.2018.06.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study convexity properties of energy functions in plane nonlinear elasticity of incompressible materials and show that rank-one convexity of an objective and isotropic elastic energy W on the special linear group SL(2) implies the polyconvexity of W. (C) 2018 Elsevier Masson SAS. All rights reserved.

引用

页码：88 / 104

页数：17

共 53 条

[1] DISCONTINUOUS DEFORMATION GRADIENTS IN PLANE FINITE ELASTOSTATICS OF INCOMPRESSIBLE MATERIALS [J].