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A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

Author

Listed:
  • Lei Lan

    (School of Innovation and Entrepreneurship, Wuhan Railway Vocational College of Technology, Wuhan 430205, China)

  • Jiaqi Zhou

    (Hubei Provincial Key Laboratory of Chemical Equipment Intensification and Intrinsic Safety, School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China)

  • Wanrong Xu

    (Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China)

  • Gongbo Long

    (Hubei Provincial Key Laboratory of Chemical Equipment Intensification and Intrinsic Safety, School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
    Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China)

  • Boqi Xiao

    (Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong, China)

  • Guanshui Xu

    (Department of Mechanical Engineering, The University of California, Riverside, CA 92521, USA)

Abstract

Crack problems in multilayered elastic media have attracted extensive attention for years due to their wide applications in both a theoretical analysis and practical industry. The boundary element method (BEM) is widely chosen among various numerical methods to solve the crack problems. Compared to other numerical methods, such as the phase field method (PFM) or the finite element method (FEM), the BEM ensures satisfying accuracy, broad applicability, and satisfactory efficiency. Therefore, this paper reviews the state-of-the-art progress in a boundary-element analysis of the crack problems in multilayered elastic media by concentrating on implementations of the two branches of the BEM: the displacement discontinuity method (DDM) and the direct method (DM). The review shows limitation of the DDM in applicability at first and subsequently reveals the inapplicability of the conventional DM for the crack problems. After that, the review outlines a pre-treatment that makes the DM applicable for the crack problems and presents a DM-based method that solves the crack problems more efficiently than the conventional DM but still more slowly than the DDM. Then, the review highlights a method that combines the DDM and the DM so that it shares both the efficiency of the DDM and broad applicability of the DM after the pre-treatment, making it a promising candidate for an analysis of the crack problems. In addition, the paper presents numerical examples to demonstrate an even faster approximation with the combined method for a thin layer, which is one of the challenges for hydraulic-fracturing simulation. Finally, the review concludes with a comprehensive summary and an outlook for future study.

Suggested Citation

  • Lei Lan & Jiaqi Zhou & Wanrong Xu & Gongbo Long & Boqi Xiao & Guanshui Xu, 2023. "A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review," Mathematics, MDPI, vol. 11(19), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4125-:d:1251049
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    References listed on IDEAS

    as
    1. Wan Cheng & Chunhua Lu & Bo Xiao, 2021. "Perforation Optimization of Intensive-Stage Fracturing in a Horizontal Well Using a Coupled 3D-DDM Fracture Model," Energies, MDPI, vol. 14(9), pages 1-18, April.
    2. Jun Gao & Boqi Xiao & Biliang Tu & Fengye Chen & Yonghui Liu, 2022. "A Fractal Model For Gas Diffusion In Dry And Wet Fibrous Media With Tortuous Converging–Diverging Capillary Bundle," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-10, December.
    3. Boqi Xiao & Qiwen Huang & Hanxin Chen & Xubing Chen & Gongbo Long, 2021. "A Fractal Model For Capillary Flow Through A Single Tortuous Capillary With Roughened Surfaces In Fibrous Porous Media," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-10, February.
    4. Gongbo Long & Yingjie Liu & Wanrong Xu & Peng Zhou & Jiaqi Zhou & Guanshui Xu & Boqi Xiao, 2022. "Analysis of Crack Problems in Multilayered Elastic Medium by a Consecutive Stiffness Method," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
    5. Boqi Xiao & Peilong Wang & Jinsui Wu & Huaizhi Zhu & Mingxing Liu & Yonghui Liu & Gongbo Long, 2022. "A Novel Fractal Model For Gas Diffusion Coefficient In Dry Porous Media Embedded With A Damaged Tree-Like Branching Network," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-15, November.
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