An X-FEM approach for large sliding contact along discontinuities

The extended finite element method (X‐FEM) has been developed to minimize requirements on the mesh design in a problem with a displacement discontinuity. This advantage, however, still remains limited to the small deformation hypothesis when considering sliding discontinuities. The approach presented in this paper proposes to couple X‐FEM with a Lagrangian large sliding frictionless contact algorithm. A new hybrid X‐FEM contact element was developed with a contact search algorithm allowing for an update of contacting surfaces pairing. The stability of the contact formulation is ensured by an algorithm for fulfilling Ladyzhenskaya‐Babuska‐Brezzi (LBB) condition. Several 2D simple examples are presented in this paper in order to prove its efficiency and stability. Copyright © 2008 John Wiley & Sons, Ltd.