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.
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 |