Level set topology optimization of problems with sliding contact interfaces

This paper introduces a topology optimization method for the design of two-component structures and two-phase material systems considering sliding contact and separation along interfaces. The geometry of the contact interface is described by an explicit level set method which allows for both shape and topological changes in the optimization process. The mechanical model assumes infinitesimal strains, a linear elastic material behavior, and a quasi-static response. The contact conditions are enforced by a stabilized Lagrange multiplier method and an active set strategy. The mechanical model is discretized by the extended finite element method which retains the crispness of the level set geometry description and allows for the convenient integration of the weak form of the contact conditions at the phase boundaries. The formulation of the optimization problem is regularized by introducing a perimeter penalty into the objective function. The optimization problem is solved by a nonlinear programming scheme computing the design sensitivities by the adjoint method. The main characteristics of the proposed method are studied by numerical examples in two dimensions. Consideration of contact leads to the formation of barb-type features that increase the interface stiffness. The numerical results further demonstrate the significant difference in the optimized geometries when assuming perfect bonding versus considering contact.