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Zeitschrift für Analysis und ihre Anwendungen


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Volume 34, Issue 4, 2015, pp. 391–418
DOI: 10.4171/ZAA/1546

Published online: 2015-10-29

Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening II: Regularization and Differentiability

Gerd Wachsmuth[1]

(1) Technische Universität Chemnitz, Germany

We consider an optimal control problem governed by an evolution variational inequality arising in quasistatic plasticity with linear kinematic hardening. A regularization of the time-discrete problem is derived. The regularized forward problem can be interpreted as system of coupled quasilinear PDEs whose principal parts depend on the gradient of the state. We show the Fréchet differentiability of the solution map of this quasilinear system. As a consequence, we obtain a first order necessary optimality system. Moreover, we address certain convergence properties of the regularization.

Keywords: Complementarity condition, quasistatic plasticity, time-dependent variational inequality, mathematical program with complementarity constraints, evolution variational inequality, rate-independent

Wachsmuth Gerd: Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening II: Regularization and Differentiability. Z. Anal. Anwend. 34 (2015), 391-418. doi: 10.4171/ZAA/1546