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A method to treat frictional contact problems along embedded surfaces in thefinite element framework is developed. Arbitrarily shaped embedded surfaces,cutting through finite element meshes, are handled by the X-FEM. The frictionalcontact problem is solved using the monolithic augmented Lagrangian methodwithin the mortar framework which was adapted for handling embedded surfaces.We report that the resulting mixed formulation is prone to mesh locking in caseof high elastic and mesh density contrasts across the contact interface. Themesh locking manifests itself in spurious stress oscillations in the vicinityof the contact interface. We demonstrate that in the classical patch test,these oscillations can be removed simply by using triangular blending elements.In a more general case, the triangulation is shown inefficient, thereforestabilization of the problem is achieved by adopting a recently proposedcoarse-graining interpolation of Lagrange multipliers. Moreover, we demonstratethat the coarse-graining is also beneficial for the classical mortar method toavoid spurious oscillations for contact interfaces with high elastic contrast.The performance of this novel method, called MorteX, is demonstrated on severalexamples which show as accurate treatment of frictional contact along embeddedsurfaces as the classical mortar method along boundary fitted surfaces.

MorteX method for contact along real and embedded surfaces: coupling X-FEM with the Mortar method