An unconstrained integral approximation of large sliding frictional contact between deformable solids

This paper presents a new integral approximation of frictional contact problems under finite deformations and large sliding. Similar to other augmented Lagrangian based formulations, the proposed method expresses impenetrability, friction and the relevant complementarity conditions as a non-smooth equation, consistently linearized and incorporated in a generalized Newton solution process. However, instead of enforcing the non-smooth complementarity equation in the already discretized system, a corresponding weak formulation in the continuous setting is considered and discretized through a standard Galerkin procedure. Such an integral handling of the contact and friction complementarity conditions, applied previously only to frictional contact problems under small deformations, is extended in the present paper to contact with Coulomb friction between solids undergoing large deformations. In total, the proposed method is relatively simple to implement, while its robustness is illustrated through numerical examples in two and three dimensions.