Filters

2008 - 200912010 - 20151

More filters

20192
Reset filters

Settings

Subject: Rate-independent processes ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit
    (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.
  • Thumbnail Image
    Item
    Coupling rate-independent and rate-dependent processes: Existence results
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Rossi, Riccarda; Thomas, Marita
    We address the analysis of an abstract system coupling a rate-independent process with a second order (in time) nonlinear evolution equation. We propose suitable weak solution concepts and obtain existence results by passing to the limit in carefully devised time-discretization schemes. Our arguments combine techniques from the theory of gradient systems with the toolbox for rate-independent evolution, thus reflecting the mixed character of the problem. Finally, we discuss applications to a class of rate-independent processes in visco-elastic solids with inertia, and to a recently proposed model for damage with plasticity.