Analysis and Numerical Techniques for Optimal Control Problems Involving Variational Inequalities Arising in Elastoplasticity

点击翻译按钮获取中文摘要

Solid bodies depart from their rest shape under the influence of applied loads. In case the applied loads or stresses are sufficiently small, many solids exhibit a linearly elastic and reversible behavior. If, however, the stress induced by the applied loads exceeds a certain threshold (the yield stress), the material behavior switches from the elastic to the so-called plastic regime. In this state, the overall loading process is no longer reversible and permanent deformations remain even after the loads are withdrawn. Mathematically, this leads to a description involving variational inequalities.Plastic deformation is desired for instance as an industrial shaping technique of metal workpieces. The task of finding appropriate time-dependent loads which effect a desired final deformation leads to optimal control problems for elastoplasticity systems. The main goals of this project are to investigate these optimization problems, to quantify the error due to discretization, and to develop fast algorithms for their solution.