An optimal control problem in polyconvex hyperelasticity

Please always quote using this URN: urn:nbn:de:0297-zib-14745
  • 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:ZIB-Report
Tag:implant design; optimal control; polyconvex elasticity
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J20 Optimal control problems involving partial differential equations
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Bxx Elastic materials / 74B20 Nonlinear elasticity
Date of first Publication:2012/02/24
Series (Serial Number):ZIB-Report (12-08)