If the unilateral constraints are modelled by the continuum mechanics based contact models, the contact forces can be computed directly through an explicit mathematical formula, that depends on the contact model of choice. If instead the non-smooth theory based method is employed, there are two main formulations for the solution of the Signorini conditions: the nonlinear / linear complementarity problem (N/LCP) formulation and the augmented Lagrangian formulation. With respect to the solution of contact models, the non-smooth method is more tedious, but less costly from the computational viewpoint. A more detailed comparison of solution methods using contact models and non-smooth theory was carried out by Pazouki et al.