A mortar based approach for the enforcement of periodic boundary conditions on arbitrarily generated meshes

A new approach for the enforcement of periodic boundary conditions on representative volume element (RVE) problems is presented. The strategy is based on a mortar formulation and considers two and three dimensional problems in the finite deformation frame. The mortar discretization is combined with the Lagrange multiplier method for the enforcement of periodicity constraints at each pair of corresponding boundaries of the RVE in a weak integral sense. The interpolation of the Lagrange multipliers is undertaken with dual shape functions, which can be locally eliminated from the RVE system of equations by static condensation, avoiding an increase on the system size. The numerical treatment within a Newton-based finite element solution procedure for the RVE equilibrium problem is discussed in detail. The resulting method is able to efficiently enforce periodic configurations over complex RVEs at finite strains with arbitrarily generated finite element meshes. Several numerical examples are presented to demonstrate the robustness of the method and the quality of results.