## Title data

Lubkoll, Lars ; Schiela, Anton ; Weiser, Martin:

**An optimal control problem in polyconvex hyperelasticity.**

*In:* SIAM Journal on Control and Optimization.
Vol. 52
(2014)
Issue 3
.
- pp. 1403-1422.

ISSN 1095-7138

DOI: https://doi.org/10.1137/120876629

Review: |

## Related URLs

## Project information

Project title: |
Project's official title Project's id DFG Research Center Matheon "Mathematics for key technologies" FZT 86 |
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Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

We consider an implant shape design problem arising in the context of facial surgery. The aim is to find the shape of an implant that deforms the soft tissue of the skin in a desired way. Assuming sufficient regularity, we introduce a reformulation as an optimal control problem where the control acts as a boundary force. The solution of that problem can be used to recover the implant shape from the optimal state. For a simplified problem, in the case where the state can be modeled as a minimizer of a polyconvex hyperelastic energy functional, we show existence of optimal solutions and derive---on a formal level---first order optimality conditions. Finally, preliminary numerical results are presented for the original optimal control formulation.