Rate independent evolutions are inherently nonsmooth. In this talk we present results concerning weak differentiability properties of such evolutions resp. the solution operator of the associated variational inequality. In particular, we discuss whether these operators are semismooth.
joint work with Andreas Fischer
Recently, a Newton-type method for the solution of Karush-Kuhn-Tucker system has been developed, that builds on the reformulation of the system as system of nonlinear equations by means of the Fischer-Burmeister function. Based on a similar idea, we propose a constrained Levenberg-Marquardt-type method for solving a general nonlinear complementarity problem. We show that this method is locally superlinear convergent under certain conditions which allow nonisolated and degenerate solutions.
joint work with Stefan Ulbrich
We consider the optimal control of elastoplasticity problems with large deformations motivated by engineering applications. To solve the optimal control problem, we need to handle the occurring flow rule within the simulation. Therefore we analyze different solution approaches which are motivated by methods applied in linear elastoplasticity but extended to the case of a multiplicative split of the deformation gradient. Due to the high complexity of the resulting model, we include reduced order models to speed up the simulation process. We present theoretical as well as computational aspects.