(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Mielke, Alexander; Petrov, Adrien; Martins, João A.C.
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.
