A domain decomposition algorithm for contact problems with Coulomb’s friction

Contact problems of elasticity are used in many fields of science and engineering, especially in structural mechanics, geology and biomecanics. Many numerical procedures solving contact problems have been proposed in the engineering literature. They are based on standard discretization techniques for partial differential equations in combination with a special implementation of non-linear contact conditions (e.g., see [3, 5, 6, 8]). The use of domain decomposition methods turns out to be one of the most efficient approaches. Recently, Dirichlet-Neumann and FETI type algorithms have been proposed and studied for solving multibody contact problems with Coulomb friction (see for example [7, 1, 2]). In this paper, the Neumann-Neumann algorithm is extended to two-body contact problems with Coulomb friction. The main difficulty is due to the boundary conditions at the contact interface. They are highly non-linear, both in the normal direction (unilateral contact conditions) and in the tangential one (Coulomb’s law). A fixed point procedure is introduced to ensure the continuity of the contact stresses. Numerical results illustrate that an optimal relaxation parameter exists and its value is nearly independent of the friction coefficient and the mesh size.