A Note on Strong Ellipticity in Two-Dimensional Isotropic Elasticity

被引：9

作者：

De Tommasi, Domenico ^{[1
]}

Puglisi, Giuseppe ^{[1
]}

Zurlo, Giuseppe ^{[1
]}

机构：

[1] Politecn Bari, Dipartimento Ingn Civile & Ambientale, Bari, Italy

来源：

JOURNAL OF ELASTICITY | 2012年 / 109卷 / 01期

关键词：

Strong ellipticity; Nonlinear elasticity; Isotropic materials; Plane deformations; SUFFICIENT CONDITIONS; PLANE-STRAIN; ELASTOSTATICS;

D O I：

10.1007/s10659-011-9370-1

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Based on the choice of two physically meaningful strain measures, we study necessary and sufficient conditions for strong ellipticity of the equilibrium equations for two-dimensional isotropic hyperelastic bodies. Specifically, we show, depending on the values of the derivatives of the energy function, that strong ellipticity is equivalent to a single condition with a clear physical interpretation.

引用

页码：67 / 74

页数：8

共 15 条

[1] [Anonymous], 1965, ENCY PHYS
[2] A NOTE ON UNDISTORTED STATES OF ISOTROPIC ELASTIC SOLIDS
ARON, M
[J]. JOURNAL OF ELASTICITY, 1988, 19 (02) : 179 - 187
[3] NECESSARY AND SUFFICIENT CONDITIONS FOR ISOTROPIC RANK-ONE CONVEX-FUNCTIONS IN DIMENSION-2
AUBERT, G
[J]. JOURNAL OF ELASTICITY, 1995, 39 (01) : 31 - 46
[4] BIFURCATION TO PEAR-SHAPED EQUILIBRIA OF PRESSURIZED SPHERICAL MEMBRANES
CHEN, YC
HEALEY, TJ
[J]. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1991, 26 (3-4) : 279 - 291
[5] Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension
Dacorogna, B
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2001, 1 (02): : 257 - 263
[6] A SIMPLE DERIVATION OF NECESSARY AND SUFFICIENT CONDITIONS FOR THE STRONG ELLIPTICITY OF ISOTROPIC HYPERELASTIC MATERIALS IN PLANE-STRAIN
DAVIES, PJ
[J]. JOURNAL OF ELASTICITY, 1991, 26 (03) : 291 - 296
[7] Damage and healing effects in rubber-like balloons
De Tommasi, D.
Marzano, S.
Puglisi, G.
Zurlo, G.
[J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2009, 46 (22-23) : 3999 - 4005
[8] Ericksen J.L., 1991, INTRO THERMODYNAMICS
[9] A note on uniqueness in linear elastostatics
Fosdick, Roger
Piccioni, M. D.
Puglisi, G.
[J]. JOURNAL OF ELASTICITY, 2007, 88 (01) : 79 - 86
[10] HAYES M, 1969, ARCH RATION MECH AN, V33, P181

← 1 2 →