Lipschitz Lectures

Modeling and analysis of rate-independent processes

Alexander Mielke


Date: January 8-23 2007
Location: Kleiner Hörsaal, Wegelerstr. 10, Bonn

Abstract:

Some physical processes like dry friction, elastoplasticity, damage, hysteresis in ferromagnets and shape-memory alloys can be modeled by rateindependent material laws. We provide mathematical models for such processes and discuss general existence results based on the energetic formulation which is based on the dissipation distance and the stored-energy funtional and thus constitutes a "variational evolution" like gradient flows.
Several applications are given and the question of convergence of solutions under Gamma convergence of the functionals is addressed. The latter theory provides convergence of numerical schemes and homogenization results.