Improved XFEM (IXFEM): Arbitrary multiple crack initiation, propagation and interaction analysis

An improved XFEM (IXFEM) is developed for the analysis of arbitrary multiple crack initiation, propagation, and interaction in two-dimensional (2-D) elastic solids. The proposed method couples the IXFEM (Tian and Wen, 2015; Tian et al., 2019) and the level set templated cover cutting method (LSTCCM) previously proposed by the authors (Wen et al., 2023). The issues of the standard XFEM arising in a multiple crack simulation, such as the difficulty of level set combination and the more severe ill -conditioning of the global stiffness matrix, are fundamentally eliminated through the above methodology. The crack -tip singularity enrichment is introduced to maintain high accuracy through an extra-DOF-free PU approximation (Tian, 2013). The LSTCCM is substantially enhanced by introducing novel techniques for treating (a) crack kinking and branching, (b) crack junction and intersection, and (c) crack tip movement and coalescence. After the above treatments, the LSTCCM is extended to model the geometry of 2-D evolving cracks in this paper. In addition, an adaptive interaction integral is empirically established for accurately evaluating the stress intensity factors (SIFs) of crack tips close to other cracks or crack tips. To facilitate the analysis of competing cracks, a prediction-correction scheme is proposed based on a set of turning point search algorithms. A calibration-verification- validation benchmarking system is carefully designed, and it highly demonstrates the accuracy, effectiveness, robustness, and reliability of the present approach.