An optimal control problem in polyconvex hyperelasticity
- We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled 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.
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| Author: | Lars Lubkoll, Anton Schiela, Martin WeiserORCiD |
|---|---|
| Document Type: | Article |
| Parent Title (English): | SIAM J. Control Opt. |
| Volume: | 52 |
| Issue: | 3 |
| First Page: | 1403 |
| Last Page: | 1422 |
| Year of first publication: | 2014 |
| Page Number: | 20 |
| Preprint: | urn:nbn:de:0297-zib-14745 |
| DOI: | https://doi.org/10.1137/120876629 |
