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 that describes 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: the direct optimization method, the augmented Lagrangian method and the primal–dual active set strategy. • Mathematical modeling of the body's behavior on the contact boundary is challenging. • Contact phenomena described by nonmonotone laws require special numerical treatment. • Nonsmooth nonconvex hemivariational problems need sophisticated methods. • Knowing the properties of algorithms for specific problems is crucial in applications. [ABSTRACT FROM AUTHOR]