Simulation of Plastic Fatigue Crack Growth by a Two Scale Extended Finite Element Method

A new technique for the finite element modelling of elastic-plastic fatigue crack growth with frictional contact on the crack faces is presented. The eXtended Finite Element Method (X-FEM) is used to discretize the equations, allowing for the modelling of arbitrary cracks whose geometry are independent of the finite element mesh. This paper presents an augmented Lagrangian formulation in the X-FEM framework in order to simulate elastic-plastic crack growth with treatment of contact and friction. The original formulation, which takes advantages of a coarse and a fine mesh close to the crack tip, is presented. In a second time the numerical issues such as contact treatment and numerical integration are adressed, and finally numerical examples are shown to validate the method.