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

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
348
Issue
2
Identifiers
DOI: 10.1016/j.jmaa.2008.07.077
Keywords
  • Rate-Independent Processes
  • Quasi-Static Problems
  • Differential Inclusions
  • Elastoplasticity
  • Hardening
  • Variational Formulations
  • Slow Time Scale

Abstract

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 tend to 0. An application to three-dimensional elastic-plastic systems with hardening is given.

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