Three-dimensional fracture propagation with numerical manifold method

• Published in: Engineering analysis with boundary elements Vol. 72; pp. 65 - 77
• Main Authors: Yang, Yongtao, Tang, Xuhai, Zheng, Hong, Liu, Quansheng, He, Lei
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2016
• Subjects: Algorithms; Crack initiation; Crack propagation; Fracture mechanics; Fracture propagation; Manifolds (mathematics); Mathematical analysis; Mathematical models; Maximum tensile stress criterion; Numerical manifold method (NMM); Tensile stress; Three dimensional simulation; Maximum tensile stress criterion; Numerical manifold method (NMM); Three dimensional simulation; Fracture propagation
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2016.08.008

By introducing the concept of mathematical cover and physical cover, the numerical manifold method (NMM) is able to solve continuous and discontinuous problems in a unified way. In this paper, the NMM is developed to analyze three dimensional (3D) fracture propagation. The maximum tensile stress criterion is implemented to determine whether the fracture will propagate and the direction of fracture propagation. Three benchmark problems are analyzed to validate the present algorithm and program. The numerical results replicate available experimental results and existing numerical results. The present algorithm and 3D NMM code are promising for 3D fracture propagation. They deserve to be further developed for the analysis of rock mechanic problems in which the initiation and propagation of multiple fractures, tensile and shear fractures, and fracture propagation under compressive loading are taken into account.