Fast and robust level set update for 3D non-planar X-FEM crack propagation modelling

In the X-FEM framework, the need to represent a discontinuity independently of the structural mesh relies on the level set technique. Hence crack propagation can be simulated by an update of two distinct level sets, the evolution of which is described by differential equations. The aim of this paper is to analyse the resolution of these equations in order to formulate a robust and fast numerical process allowing 3D crack propagation simulations even in presence of high kink angles occurring in mixed mode propagation. The numerical integration is accomplished by means of a robust finite difference upwind scheme applied to an auxiliary regular grid. An alternative level set update equation and a fast localisation of the integration domain, specifically developed for crack propagation problems, are formulated and proposed in the paper in order to gain in stability, robustness and performance.