Optimal Control of Quasistatic Plasticity

Gerd Wachsmuth*

An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of quasistatic elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. By showing that the VI can be written as an evolutionary variational inequality, we obtain the continuity of the forward operator. This is the key step to prove the existence of minimizers. In order to derive necessary optimality conditions, a family of time discretized and regularized optimal control problems is analyzed. By passing to the limit in the optimality conditions for the regularized problems, necessary optimality conditions of weakly stationarity type are obtained. We present a solution method which builds upon the optimality system of the time discrete and regularized problem. Numerical results which illustrates the possibility of controlling the springback effect are presented.

Mathematics Subject Classification: 49K20

Keywords: quasistatic plasticity; optimal control

Minisymposion: Optimal Control of Time-Dependent Variational Inequalities