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Numerical simulation for quasi-static crack growth and dynamic crack branching by coupled state-based PD and XFEM

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Abstract

This paper presents a novel framework combining the state-based peridynamics (SBPD) with the extended finite element method (XFEM) for crack propagation in two-dimensional solids. Numerical examination is conducted fulfilling both the quasi-static and time-dependent loading conditions. The computational domain is partitioned into two regions: (a) SPBD region: the vicinity of crack tips and potential region where the crack is likely to propagate, and (b) XFEM region: the area behind the crack tip and the rest of the body. The salient features of the developed framework include: (a) avoiding requirement of a priori knowledge of enrichment functions like the conventional XFEM; (b) without fracture criteria for crack propagation; (c) no restriction on the value of Poisson’s ratio like the bond-based peridynamics; and (d) higher computational efficiency than the pure peridynamics. The efficiency and accuracy of the proposed framework are systematically demonstrated through benchmark examples involving quasi-static crack growth and dynamic crack branching problems.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11932006). The financial supports are gratefully acknowledged.

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Authors and Affiliations

  1. College of Mechanics and Materials, Hohai University, Nanjing, 211100, People’s Republic of China

    Bing Chen, Tiantang Yu & Qing Zhang

  2. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

    Sundararajan Natarajan

  3. Duy Tan Research Institute for Computational Engineering (DTRICE), Duy Tan University, 6 Tran Nhat Duat, Dist. 1, Ho Chi Minh City, Viet Nam

    Tinh Quoc Bui

  4. Faculty of Civil Engineering, Duy Tan University, Da Nang City, 550000, Viet Nam

    Tinh Quoc Bui

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  1. Bing Chen
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  2. Tiantang Yu
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  4. Qing Zhang
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Correspondence to Tiantang Yu or Tinh Quoc Bui.

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Chen, B., Yu, T., Natarajan, S. et al. Numerical simulation for quasi-static crack growth and dynamic crack branching by coupled state-based PD and XFEM. Acta Mech 234, 3605–3622 (2023). https://doi.org/10.1007/s00707-023-03585-4

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  • DOI: https://doi.org/10.1007/s00707-023-03585-4

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