Optimal control of rate-independent systems with non-convex energies
Tuesday, 2.7.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Rate-independent systems arise in multiple applications, in particular in computational mechanics. They model processes, which are invariant w.r.t. time transformations of external loads. In some applications such as perfect plasticity or brittle damage, the stored energy functional is not uniformly convex. In this case one cannot expect uniqueness and continuity (in time) of solutions. In particular due to the lack of continuity, a variety of solutions concepts has been developed in the recent past, among them global energetic solutions and parametrized balanced viscosity solutions. In the talk, we will consider optimal control problems governed by rate-independent systems with energy functionals that are not uniformly convex. The external loads will serve as control variables. Due to the lack of uniqueness of solutions, we regularize the state equation by adding viscosity. The main part of the talk will then be concerned with the viscosity limit, i.e., we will discuss, if, and under which conditions, solutions of the optimal control problems under consideration can be approximated via viscous regularization.
Generative Models for the Design of Mechanical Metamaterials
Tuesday, 16.7.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10