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Mielke, Alexander [Author]; Petrov, Adrien [Author]; Martins, João A.C. [Author]

Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit - [published Version]

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  • Media type: Text; E-Book; Report
  • Title: Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit
  • Contributor: Mielke, Alexander [Author]; Petrov, Adrien [Author]; Martins, João A.C. [Author]
  • imprint: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008
  • Issue: published Version
  • Language: English
  • DOI: https://doi.org/10.34657/2159
  • ISSN: 0946-8633; 0946-8633
  • Keywords: slow time scale ; hardening ; Rate-independent processes ; quasi-static problems ; elastoplasticity ; variational formulations ; differential inclusions
  • Origination:
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  • Description: 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.
  • Access State: Open Access