A formulation for frictionless contact problems using a weak form introduced by Nitsche

In this paper a finite element formulation for frictionless contact problems with non-matching meshes in the contact interface is presented. It is based on a non-standard variational formulation due to Nitsche and leads to a matrix formulation in the primary variables. The method modifies the unconstrained functional by adding extra terms and a stabilization which is related to the classical penalty method. These new terms are characterized by the presence of contact forces that are computed from the stresses in the continuum elements. They can be seen as a sort of Lagrangian-type contributions. Due to the computation of the contact forces from the continuum elements, some additional degrees-of-freedom are involved in the stiffness matrix parts related to contact. These degrees-of-freedom are associated with nodes not belonging to the contact surfaces.