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This work deals with shape optimization for contact mechanics. Morespecifically, the linear elasticity model is considered under the smalldeformations hypothesis, and the elastic body is assumed to be in contact(sliding or with Tresca friction) with a rigid foundation. The mathematicalformulations studied are two regularized versions of the original variationalinequality: the penalty formulation and the augmented Lagrangian formulation.In order to get the shape derivatives associated to those twonon-differentiable formulations, we follow an approach based on directionalderivatives \cite{chaudet2020shape,chaudet2021shape}. This allows us to developa gradient-based topology optimization algorithm, built on these derivativesand a level-set representation of shapes. The algorithm also benefits from amesh-cutting technique, which gives an explicit representation of the shape ateach iteration, and enables us to apply the boundary conditions strongly on thecontact zone. The different steps of the method are detailed. Then, to validatethe approach, some numerical results on two-dimensional and three-dimensionalbenchmarks are presented.

A shape optimization algorithm based on directional derivatives for three-dimensional contact problems