An augmented Lagrangian contact formulation for frictional discontinuities with the extended finite element method

• An Uzawa-type augmented Lagrangian X-FEM for modeling frictional contact.
• A symmetrized (nested) approach to implement a return mapping algorithm for Coulomb friction rule.
• Adapting the vital vertex algorithm to robustly impose the contact constraints in ALM framework.
• The accuracy of proposed model by simulation of straight, curved and wave-shaped discontinuities.

In this paper, an Uzawa-type augmented Lagrangian contact formulation is presented for modeling frictional discontinuities in the framework of the X-FEM technique. The kinematically nonlinear contact problem is resolved based on an active set strategy to fulfill the Kuhn–Tucker inequalities in the normal direction of contact. The Coulomb’s friction rule is employed to address the stick–slip behavior on the contact interface through a return mapping algorithm in conjunction with a symmetrized (nested) augmented Lagrangian approach. A stabilization algorithm is proposed for the robust imposition of the frictional contact constraints within the proposed augmented Lagrangian framework. Several numerical examples are presented to demonstrate various aspects of the proposed computational algorithm in simulation of the straight, curved and wave-shaped discontinuities.