A survey of numerical methods for hemivariational inequalities with applications to Contact Mechanics

In this paper we present an abstract nonsmooth optimization problem for which we recall existence and uniqueness results. We show a numerical scheme to approximate its solution. The theory is later applied to a sample static contact problem describing an elastic body in frictional contact with a foundation. This problem leads to a hemivariational inequality which we solve numerically. Finally, we compare three computational methods of solving contact mechanical problems: direct optimization method, augmented Lagrangian method and primal-dual active set strategy.