Mortar based frictional contact formulation for higher order interpolations using the moving friction cone

Finite element discretizations including contact usually apply the standard NTS-(node-to-segment) element. Thus, a coupling with higher order solid elements leads to inconsistencies in the transmission of contact stresses. One can circumvent this using the mortar method which includes a weak projection of the contact constraints.In this paper we present a penalty formulation based on the mortar concept for two-dimensional large deformation frictional contact. The discretization of the contact surfaces contains quadratic approximations which can be used within a quadratic approximation of the solid elements. To obtain a simple and efficient matrix formulation, the moving friction cone algorithm is applied.