A Local Multi-grid X-FEM approach for 3D fatigue crack growth

Abstract

One proposes a local multi-grid X-FEM method for 3-D crack propagation simulation in large structures. Enrichments allow the asymptotic behaviour on the crack front to be well described and the structure doesn’t need to be remeshed during the crack propagation. However, the different scales involved in fracture mechanics problems can differ from several orders of magnitude and industrial meshes are usually not designed to take into account small cracks. Enrichments are therefore useless if the crack is too small compared to the element size. The X-FEM is thus coupled with a local multi-grid algorithm. The link between the scale of the structure and the scale of the crack is hence possible. Moreover, multi-grid techniques are very efficient in term of cpu time. The coupling of X-FEM with the multi-grid algorithm is then described and specific computational aspects that deal with intergrid operators, the multi-scale enrichment strategy and level sets are pointed out. In particular, a specific enrichment strategy, based on a multi-grid convergence rate criterion is proposed. Furthermore, the use of a single independent structured mesh for the level sets description is shown to be very robust and accurate. Finally, examples that illustrate the good accuracy and efficiency of the method are given and especially in the case of 3D fatigue crack propagation.