A novel boundary tracing method without enrichment for modeling cracks and their propagation

Abstract

A novel direct numerical modeling method for preexisting cracks and their propagation is developed based on the integral-generalized finite difference (IGFD) method which has an excellent performance in accuracy, flexibility, and convenience in dealing with boundary conditions. “Direct modeling” means discontinuities and their propagation are directly treated as boundaries of subdomains. The standard IGFD method for continuity problems is adopted in regions far from discontinuities, while modifications are required around the discontinuities. Some special treatments such as paired nodes and birth–death algorithms are employed to characterize the existing cracks and track the crack growth path. These techniques together constitute the extended IGFD (xIGFD) method realizing the application of IGFD method in discontinuity problems. Three specific technologies, xIGFD-A, xIGFD-B, and xIGFD-C are proposed to treat the growing nodes along the discontinuities. The xIGFD-A needs to number the newly generated nodes and add degrees of freedom for propagating cracks, which would change the dimensions of the global matrices, while the xIGFD-B and the xIGFD-C do not. The successful applications of this proposed xIGFD method as well as the comparisons with existing numerical methods in a series of examples involving quasi-static propagation of a single crack and cross cracks have fully proved its effectiveness and superiority. The proposed method neither needs enriched basis functions based on prior knowledge nor requires re-meshing operations, which shows the unity and conciseness of the discretization scheme for continuity and discontinuity problems. Therefore, it has application potential in more complex practical problems like hydraulic fracturing and fatigue cracks.