Implementation of hybrid crack element on a general finite element mesh and in combination with XFEM

The hybrid crack element (HCE) is one of the most accurate and convenient finite elements (FEs) for the direct calculation of the stress intensity factor (SIF) and coefficients of the higher order terms of the Williams expansion. In its implementation, the HCE is generally designed first at each crack tip and then the whole domain is meshed taking into account the boundaries of the domain as well as those of the HCE. This complicates the meshing task and hinders the incorporation of the HCE into commercial FE packages. In this paper, the implementation of the HCE on a general FE mesh and its incorporation into commercial FE packages is detailed and extensively validated. Furthermore, it is shown how to couple the HCE with the extended/generalized finite element method (XFEM). The HCE is used for the crack tip region, while the XFEM is used for modelling crack faces outside the HCE independent of the mesh with jump functions. The coupled method retains the advantages of both the HCE and XFEM. Numerical results are presented to validate the coupled method.