Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit
- Mielke, Alexander
- Petrov, Adrien
- Martins, Joao A. C.
2010 Mathematics Subject Classification
- 34A60, 47H06, 73E50, 73E99, 74C05
- Rate-independent processes, quasi-static problems, differential inclusions,, elastoplasticity, hardening, variational formulations, slow time scale.
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.
- J. Math. Anal. Appl., 348 (2008) pp. 1012--1020.