Improved XFEM (IXFEM): An Accurate and Efficient Approach for Arbitrary Multiple Crack Analyses under Static and Cyclic Loading
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The extended finite element method (XFEM) is a prominent technique for crack analysis; however, its application to problems involving arbitrary multiple cracks remains challenging. Key limitations include the linear dependence and ill-conditioning of the global stiffness matrix, as well as the complex geometric descriptions of interacting cracks. To overcome these challenges, this work presents an Improved XFEM (IXFEM) framework. First, the IXFEM formulation [1,2] is extended to multiple-crack problems, effectively eliminating numerical instabilities related to linear dependence and ill-conditioning. Second, a novel level-set templated cover cutting method (LSTCCM) [3] is introduced to robustly describe arbitrary crack geometries by combining the advantages of the level-set method and cover cutting technique. Furthermore, it incorporates novel techniques for modelling multiple evolving cracks, such as a prediction–correction scheme for competing crack paths [4], and extends to simulate high-cycle fatigue crack growth under cyclic loading by integrating accurate fatigue crack update schemes [5]. Numerical results demonstrate that the developed approach is accurate, efficient, robust, and reliable for analyzing arbitrary multiple crack propagation in 2D elastic solids under both static and cyclic loads. Ongoing work focuses on extending this framework to multi-physics fracture problems, such as hydraulic fracturing [6], where it shows promising potential for coupled simulations.
