A generalized cover renewal strategy for multiple crack propagation in two-dimensional numerical manifold method

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.