  An equilibrium of a linear elastic body subject to loading and satisfying the
friction and contact conditions can be described by a variational inequality of
the second kind and the respective discrete model attains the form of a
generalized equation. To its numerical solution we apply the semismooth* Newton
method by Gfrerer and Outrata (2019) in which, in contrast to most available
Newton-type methods for inclusions, one approximates not only the single-valued
but also the multi-valued part. This is performed on the basis of limiting
(Morduchovich) coderivative. In our case of the Tresca friction, the
multi-valued part amounts to the subdifferential of a convex function generated
by the friction and contact conditions. The full 3D discrete problem is then
reduced to the contact boundary. Implementation details of the semismooth*
Newton method are provided and numerical tests demonstrate its superlinear
convergence and mesh independence.
