A dual Lagrange method for contact problems with regularized contact conditions

This paper presents an algorithm for solving quasi-static, non-linear elasticity contact problems without friction in the context of rough surfaces. Here, we want to model the transition from soft to hard contact in case of rough surfaces on the micro-scale. The popular dual mortar method is used to enforce the contact constraints in a variationally consistent way without increasing the algebraic system size. The algorithm is deduced from a perturbed Lagrange formulation and combined with mass-lumping techniques to exploit the full advantages of the duality pairing. This leads to a regularized saddle point problem, for which a non-linear complementary function and thus a semi-smooth Newton method can be derived. Numerical examples demonstrate the applicability to industrial problems and show a good agreement to experimentally obtained results.