Quasistatic evolution problems for linearly elastic-perfectly plastic materials

被引：158

作者：

Dal Maso, G ^{[1
]}

DeSimone, A ^{[1
]}

Mora, MG ^{[1
]}

机构：

[1] Scuola Int Super Studi Avanzati, I-34014 Trieste, Italy

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2006年 / 180卷 / 02期

关键词：

D O I：

10.1007/s00205-005-0407-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This approach provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.

引用

页码：237 / 291

页数：55

共 31 条

[11]

Hill R., 1950, The Mathematical Theory of Plasticity

[12]

JOHNSON C, 1976, J MATH PURE APPL, V55, P431

[13] DUAL SPACES OF STRESSES AND STRAINS, WITH APPLICATIONS TO HENCKY PLASTICITY [J].

KOHN, R ;

TEMAM, R .

APPLIED MATHEMATICS AND OPTIMIZATION, 1983, 10 (01) :1-35

[14]

Lubliner J., 1990, PLASTICITY THEORY

[15] Existence results for energetic models for rate-independent systems [J].

Mainik, A ;

Mielke, A .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2005, 22 (01) :73-99

[16]

Martin JB., 1975, Plasticity: Fundamentals and General Results

[17]

Matthies H, 1979, ENERGY METHODS FINIT, P309

[18] Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation [J].

Miehe, C .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2002, 55 (11) :1285-1322

[19] A rate-independent model for inelastic behavior of shape-memory alloys [J].

Mielke, A ;

Roubícek, T .

MULTISCALE MODELING & SIMULATION, 2003, 1 (04) :571-597

[20] Energetic formulation of multiplicative elasto-plasticity using dissipation distances [J].

Mielke, A .

CONTINUUM MECHANICS AND THERMODYNAMICS, 2003, 15 (04) :351-382

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