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

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Date
2008
Volume
1322
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

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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Keywords
Rate-independent processes, quasi-static problems, differential inclusions, elastoplasticity, hardening, variational formulations, slow time scale
Citation
Mielke, A., Petrov, A., & Martins, J. A. C. (2008). Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit (Vol. 1322). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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