An algorithm for the numerical realization of 3D contact problems with Coulomb friction

This contribution deals with the numerical realization of static contact problems with Coulomb friction for three-dimensional elastic bodies. We first introduce auxiliary contact problems with given friction which define a mapping Φ associating with a given slip bound the normal contact stress in the equilibrium state. Solutions to contact problems with Coulomb friction are defined as fixed points of Φ and are computed by using the method of successive approximations. The mathematical model of contact problems with given friction leads to a variational inequality of the second kind. Its discretization is based on the so-called reciprocal variational formulation, i.e., the formulation in terms of the normal and tangential components of stresses on the contact boundary. Unlike the two-dimensional case, constraints imposed on the tangential components of contact stresses are quadratic. The main goal of this contribution is to show how to solve this problem by using existing fast algorithms for simple (box) constraints. Numerical experiments for several variants of our algorithm will be shown and compared.