Improved XFEM for multiple crack analysis: Accurate and efficient implementations for stress intensity factors

The extended finite element method (XFEM) has achieved unprecedented success in crack analysis. However, challenges still remain for a multiple crack simulation. One issue is the difficulty of level set construction, where cracks are generally represented by combinations of different level set functions. Another issue is the rapidly increasing condition number of the global stiffness matrix, which is even more severe than the single crack case. In order to overcome these issues, we make two improvements as follows. On the one hand, inspired by the discontinuous description via cover cutting in Numerical Manifold Method (and later phantom node method in XFEM), we propose a level set templated cover cutting method, which makes use of level set values to cut a nodal patch and then to add virtual nodes. This method, which combines the advantages of both the level set method and the cover cutting technique, is simple and straightforward to implement. The method also plays a role in templated subdivision of discontinuous elements and hence presents an efficient and robust integration scheme. On the other hand, we extend the Improved XFEM (IXFEM), previously proposed by our research group, to the scenario of multiple crack problems. The method fundamentally eliminates the daunting issues of linear dependence and ill-conditioning of the standard XFEM, because it uses an extra-dof-free singularity enrichment around the crack tip. Numerical studies on multiple crack problems show that the developed approach offers various advantages: (1) Highly accurate SIF evaluation over the standard XFEM; (2) Well-conditioning of the global stiffness matrix independent of the number of cracks - condition number being of the same order as the standard FEM; (3) Efficient and robust linear system solving and geometric computations. Thus the developed approach is well capable of modeling arbitrary multiple crack problems.(c) 2023 Elsevier B.V. All rights reserved.