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This paper presents a method for the optimization of multi-componentstructures comprised of two and three materials considering large motionsliding contact and separation along interfaces. The structural geometry isdefined by an explicit level set method, which allows for both shape andtopology changes. The mechanical model assumes finite strains, a nonlinearelastic material behavior, and a quasi-static response. Identification ofoverlapping surface position is handled by a coupled parametric representationof contact surfaces. A stabilized Lagrange method and an active set strategyare used to model frictionless contact and separation. The mechanical model isdiscretized by the extended finite element method which maintains a cleardefinition of geometry. Face-oriented ghost penalization and dynamic relaxationare implemented to improve the stability of the physical response prediction. Anonlinear programming scheme is used to solve the optimization problem, whichis regularized by introducing a perimeter penalty into the objective function.Sensitivities are determined by the adjoint method. The main characteristics ofthe proposed method are studied by numerical examples in two dimensions. Thenumerical results demonstrate improved design performance when compared tomodels optimized with a small strain assumption. Additionally, examples withload path dependent objectives display non-intuitive designs.

Level set shape and topology optimization of finite strain bilateral contact problems