A two-scale extended finite element method for modelling 3D crack growth with interfacial contact

3D fatigue crack growth problems are nowadays handled using X-FEM coupled with level set techniques. It is also well established that such an approach allows mesh-independent crack modelling and no remeshing during crack propagation. However, when contact and friction occur along the crack faces, a discretization of the internal variables linked to the interface law is necessary. The interface discretization is generally constructed from the finite elements cut by the crack. As a consequence, a mesh dependency between the bulk discretization and the interface discretization is introduced. However, the dimension of the possible non-linearities arising at the crack interface (like confined plasticity or unilateral contact with friction) may be several orders of magnitude finer than the crack size. A finer discretization is thus required to accurately capture these non-linearities. The aim of the present paper is to develop a method considering the 3D cracked structure and the crack interface as two independent global and local problems characterized by different length scales and different behaviors. Here, the interface is seen as an autonomous entity with its own discretization, variables and constitutive law. A formulation involving three-fields is used. The interface is linked to the global problem in a weak sense in order to avoid instabilities in the contact solution. Two iterative strategies are considered to solve the contact problem. Two-dimensional and three-dimensional numerical examples are presented to demonstrate the ability of the model to solve the contact at the crack interface with or without propagation at a given level of accuracy.