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Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit |
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| Authors: | Alexander Mielke Adrien Petrov |
| Institution: | a Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Germany b Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany c Instituto Superior Técnico, Departamento de Engenharia Civil and ICIST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
| 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. |
| Keywords: | Rate-independent processes Quasi-static problems Differential inclusions Elastoplasticity Hardening Variational formulations Slow time scale |
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