FAU Erlangen-Nuremberg

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

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Project leaders

Fakultät für Mathematik
TU Chemnitz

Tel: +49 371 531 22530
Fax: +49 371 531 836538

Email: roland.herzog@mathematik.tu-chemnitz.de

Homepage: http://www.tu-chemnitz.de/mathematik/part_dgl

Graduate School CE
TU Darmstadt

phone: +49 6151 16 70 946
fax: +49 6151 16 44 59

email: cmeyer@gsc.tu-darmstadt.de

homepage: http://www.gsc.ce.tu-darmstadt.de/index.php?id=128

DFG funded assistants

Gerd Wachsmuth (TU Chemnitz)

Frank Schmidt (TU Chemnitz)


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state, the overall loading process is no longer reversible and permanent deformations remain even after the loads are withdrawn.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, as e.g. by deep-drawing of body sheets in the automotive industry. The task of finding appropriate time-dependent loads which effect a desired final deformation leads to optimal control problems for elastoplasticity systems. These are also motivated by the desire to reduce the amount of springback, i.e., the partial reversal of the final material deformation due to a release of the stored elastic energy once the loads are removed.

The project targets optimal control problems for static and quasi-static models of infinitesimal elastoplasticity with hardening. Its main goals are

  • to investigate these optimization problems,
  • to quantify the error due to discretization,
  • and to develop fast algorithms for their solution.

Models of elastoplasticity involve non-smooth features due to their description by variational inequalities and pointwise projections. The mathematical treatment of associated optimal control problems is therefore highly challenging and it requires a substantial extension of the established techniques.

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