A mathematical programming approach for frictional contact problems with the extended finite element method

The extended finite element method (XFEM) is a numerical method for modeling discontinuities within the classical finite element framework. This method can treat arbitrary cracks independent of the mesh and crack growth with minimal remeshing. In this paper, a nonlinear complementarity model for frictional elastic contact problems with the XFEM is presented. The conditions that describe frictional contact are formulated as a system of non-smooth equations based on variational inequality theory, and the non-smooth damped Newton method is given based on the definitions of generalized derivative to directly solve the system of equations. Finally, numerical examples are presented to demonstrate the correctness and effectiveness of this method.