Alexander Mielke

(WIAS & HU Berlin, mielke@wias-berlin.de):


Analysis of Rate-Independent Material Models.

Abstract:
Some physical processes like dry friction, elastoplasticity, damage,hysteresis in ferromagnets and shape-memory alloys can be modeled byrate-independent material laws. We provide mathematical models for suchprocesses and discuss general existence results based on the energeticformulation which is based on the dissipation distance and the stored-energyfuntional. Several applications are given and the question of convergence ofsolutions under Gamma convergence of the functionals is addressed. The latter theory provides convergence of numerical schemes and homogenization results.

Schedule:
Lecture 1 - March 3, 15:45 (room K1 at Sokolovska 83):
Classical rate-independent models including elastoplasticity (evolutionary variational inequalities, sweeping processes, differential inclusions)
Lecture 2 - March 4, 10:00 (Mathematical Institute, Zitna 25)
The energetic formulation via functionals (general theory on topological spaces, main existence result)
Lecture 3 - March 10, 17:20 (room K1)
Applications in material models (damage, hysteresis in ferroelectricity, finite-strain elastoplasticity)
Lecture 4 - March 11, 10:00 (Zitna 25)
Gamma convergence for rate-independent processes and convergence of space-time discretization
Reserve lecture March 11, 11:30-12:30



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