A generalized cover renewal strategy for multiple crack propagation in two-dimensional numerical manifold method
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A generalized cover renewal strategy for multiple crack propagation in two-dimensional numerical manifold method YU Chang-yi(于长一)1, 2, 3, 4, ZHENG Fei(郑飞)5, GUO Bing-chuan(郭炳川)2, LIU Qin-ya(刘沁雅)6 1. China Communications Construction Company-Tianjin Port Engineering Institute, Co., Ltd., Tianjin 300222, China; 2. China Communications Construction Company-First Harbor Engineering Company, Co., Ltd., Tianjin 300461, China; 3. Key Laboratory of Geotechnical Engineering, Ministry of Communications, Tianjin 300222, China; 4. Key Laboratory of Geotechnical Engineering of Tianjin, Tianjin 300222, China; 5. Institute of Continuum Mechanics, Leibniz University Hannover, 30167 Hannover, Germany; 6. Department of Physics, University of Toronto, Canada © Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract: Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system, i.e., the mathematical cover and physical cover. However, renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references. In this study, a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems. The proposed algorithm updates the cover system with a bottom-up process: 1) identification of fractured manifold elements according to the previous and latest crack tip position; and 2) local topological update of the manifold elements, physical patches, block boundary loops, and non-persistent joint loops according to the scenario classification of the propagating crack. The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis. Three crack propagation examples show that the proposed algorithm performs well in updating the cover system. This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers. Key words: numerical manifold method; multiple crack propagation; physical cover renewal; polygonal mathematical cover Cite this article as: YU Chang-yi, ZHENG Fei, GUO Bing-chuan, LIU Qin-ya. A generalized cover renewal strategy for multiple crack propagation in two-dimensional numerical manifold method [J]. Journal of Central South University, 2020, 27(8): 2367−2381. DOI: https://doi.org/10.1007/s11771-020-4455-2.
1 Introduction Crack propagation and discontinuous deformation exists in many problems in the fields of material science and geological engineering, such as failure of high strength ceramics, impact fracture of tempered glass, concrete cracking and
failure of jointed rock mass [1, 2]. The analytical solutions to crack propagation problems with complex patterns are challenging considering the complex boundary conditions, various geometrical pattern, the dynamic effects, and the no-elastic behavior. Consi
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