Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling

Abstract

Fracture modelling using numerical methods is well-advanced in 2D using techniques such as the extended nite element method (XFEM). The use of meshless methods for these problems lags somewhat behind but the potential benets of no meshing (particularly in 3D) prompt continued research into their development. In methods where the crack face is not explicitly modelled (as the edge of an element for instance) two procedures are instead used to associate the displacement jump with the crack surface: the visibility criterion and the diraction method. The visibility criterion is simple to implement and ecient to compute, especially with the help of level set coordinates. However, spurious discontinuities have been reported around crack tips using the visibility criterion, while implementing the diraction method in 3D is much more complicated than the visibility criterion. In this paper, a tying procedure is proposed to remove the diculty with the visibility criterion so that crack tip closure can be ensured while the advantages of the visibility criterion can be preserved. The formulation is based on the use of level set coordinates and the EFGM, and is generally applicable for single or multiple crack problems in 2D or 3D. The paper explains the formulation and provides verication of the method against a number of 2D crack problems.