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Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit

Please always quote using this URN:urn:nbn:de:0296-matheon-5202
  • This paper discusses the convergence of kinetic variational inequalities to rate-independent quasi-static variational inequalities. Mathematical formulations as well as existence and uniqueness results for kinetic and rate-independent quasi-static problems are provided. Sharp a priori estimates for the kinetic problem are derived that imply that the kinetic solutions converge to the rate-independent ones, when the size of initial perturbations and the rate of application of the forces tends to 0. An application to three-dimensional elastic-plastic systems with hardening is given.

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Metadaten
Author:Alexander Mielke, Adrien Petrov, Joao A. C. Martins
URN:urn:nbn:de:0296-matheon-5202
Referee:Carsten Carstensen
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/10/27
Release Date:2008/04/07
Tag:
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A60 Differential inclusions [See also 49J21, 49K21]
47-XX OPERATOR THEORY / 47Hxx Nonlinear operators and their properties (For global and geometric aspects, see 58-XX, especially 58Cxx) / 47H06 Accretive operators, dissipative operators, etc.
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Cxx Plastic materials, materials of stress-rate and internal-variable type / 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
Preprint Number:525
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