A COMPARATIVE STUDY ON 2D CRACK MODELLING USING EXTENDED FINITE ELEMENT METHOD

In general, the current crack modelling methods can be classified into two broad categories of geometrical and non-geometrical presentations. In the first category, the presence of a crack in the model is explicit and the geometry and mesh are changed during the crack growth [1,2]. In the second category, the crack does not appear in the model as a physical object but its presence affects the governing equations. These effects are either on the stress-strain constitutive equations or on the strain-displacement kinematic equations. The latter approach is implemented in the Extended Finite Element Method (XFEM) by adding extra functions (enrichment functions) to the approximation space of the elements around the crack. This process gives additional degrees of freedom to the enriched nodes. This method, which was established based on the Partition of Unity Method (PUM) and applied to fracture mechanics problems by Belytschko and Black [3], was improved by Dolbow for crack growth modelling without re-meshing [4]. The method was later applied to other problems such as 3D fracture [5], dynamic problems [6], cohesive crack modelling [7], fracture mechanics of functionally graded materials (FGM) [8], and crack modelling in orthotropic materials [9]. A very recent review of the usage of the XFEM in computational fracture mechanics is reported in ref. [10].