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Improved XFEM (IXFEM): Accurate, Efficient, Robust and Reliable Analysis for Arbitrary Multiple Crack Problems

Lixiang Wang¹, Longfei Wen^2,3, Rong Tian^2,3,*, Chun Feng^1,4,*

1 Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China
2 CAEP Software Center for High Performance Numerical Simulation, Beijing, 100088, China
3 Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China
4 School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China

* Corresponding Authors: Rong Tian; Chun Feng. Email: ;

The International Conference on Computational & Experimental Engineering and Sciences 2024, 30(3), 1-2. https://doi.org/10.32604/icces.2024.011137

Abstract

The extended finite element method (XFEM) has been successful in crack analysis but faces challenges in modeling multiple cracks. One challenge is the linear dependence and ill-conditioning of the global stiffness matrix, while another is the geometric description for multiple cracks. To address the first challenge, the Improved XFEM (IXFEM) [1–9] is extended to handle multiple crack problems, effectively eliminating issues of linear dependence and ill-conditioning. Additionally, to overcome the second challenge, a novel level set templated cover cutting method (LSTCCM) [10] is proposed, which combines the advantages of the level set method and cover cutting technique. The present approach offers highly accurate stress intensity factor evaluation, efficient linear system solving, and robust geometric computations. Furthermore, this approach introduces novel techniques for modeling multiple evolving cracks and proposes a prediction–correction scheme for competing cracks [11]. The developed approach demonstrates accuracy, effectiveness, robustness, and reliability in analyzing arbitrary multiple crack propagation problems in 2-D elastic solids. Ongoing work aims to investigate the approach for multi-physics fracture problems (e.g., hydraulic fracturing [12–14]) by coupling the present solid solver with a fluid flow solver (e.g., [15–17]), showing promise in such scenarios.

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Keywords

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