A multiscale extended finite element method for crack propagation

In this paper, we propose a multiscale strategy for crack propagation which enables one to use a refined mesh only in the crack’s vicinity where it is required. Two techniques are used in synergy: a multiscale strategy based on a domain decomposition method to account for the crack’s global and local effects efficiently, and a local enrichment technique (the X-FEM) to describe the geometry of the crack independently of the mesh. The focus of this study is the avoidance of meshing difficulties and the choice of an appropriate scale separation to make the strategy efficient. We show that the introduction of the crack’s discontinuity both on the microscale and on the macroscale is essential for the numerical scalability of the domain decomposition method to remain unaffected by the presence of a crack. Thus, the convergence rate of the iterative solver is the same throughout the crack’s propagation.