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 con- tact forces that are computed from the stresses in the contin- uum 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.