A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy

被引：5

作者：

Fiaschi, Alice ^{[1
]}

机构：

[1] SISSA, I-34014 Trieste, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2009年 / 26卷 / 04期

关键词：

Quasistatic evolution; Rate-independent processes; Elastic materials; Incremental problems; Young measures;

D O I：

10.1016/j.anihpc.2008.02.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a quasistatic evolution problem for a nonconvex elastic energy functional. Due to lack of convexity. the natural energetic formulation can be obtained only in the framework of Young measures. Since the energy functional may present multiple wells, an evolution driven by global minimizers may exhibit unnatural jumps from one well to another one, which overcome large potential barriers. To avoid this phenomenon, we study a notion of solution based on a viscous regularization. Finally we compare this solution with the one obtained with global minimization. (C) 2008 Elsevier Masson SAS. All rights reserved.

引用

页码：1055 / 1080

页数：26

共 15 条

[1] CAGNETTI F, MATH MODELS IN PRESS
[2] Quasistatic evolution problems for linearly elastic-perfectly plastic materials
Dal Maso, G
DeSimone, A
Mora, MG
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2006, 180 (02) : 237 - 291
[3] Quasistatic crack growth in nonlinear elasticity
Dal Maso, G
Francfort, GA
Toader, R
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2005, 176 (02) : 165 - 225
[4] DALMASO G, ARCH RATION IN PRESS
[5] Efendiev MA, 2006, J CONVEX ANAL, V13, P151
[6] Ekeland I., 1976, Convex Analysis and Variational Problems
[7] FIASCHI A, ESAIM COCV IN PRESS
[8] Existence results for a class of rate-independent material models with nonconvex elastic energies
Francfort, Gilles
Mielke, Alexander
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2006, 595 : 55 - 91
[9] KNEES D, 2007, INVISCID LIMIT MODEL
[10] A variational formulation of rate-independent phase transformations using an extremum principle
Mielke, A
Theil, F
Levitas, VI
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 162 (02) : 137 - 177

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