Dynamic crack propagation analysis combined the stable scheme and continuous-discontinuous cellular automaton. (January 2021)

• Record Type: Journal Article
• Authors: Yan, Fei; Zhang, Wei; Pan, Peng-Zhi; Li, Shao-Jun
• Is Part Of: Engineering fracture mechanics. Volume 241(2021)
• Publication Date: 2021-01
• Subjects: The continuous-discontinuous cellular automaton -- The stable scheme -- The adaptive updating scheme -- Dynamic crack propagation -- Numerical stability; Fracture mechanics -- Periodicals; Rupture, Mécanique de la -- Périodiques; Fracture mechanics; Periodicals; 620.112605
• DOI: 10.1016/j.engfracmech.2020.107390
• Languages: English
• ISSNs: 0013-7944

Abstract

Highlights: A fast adaptive cellular automaton model is developed for dynamic crack propagation. An adaptive enriched nodal freedom transformation is proposed. The separated time integral scheme is built respectively caused by geometric change and dynamic loading. Abstract: A continuous-discontinuous cellular automaton method (CDCA) is developed for dynamic crack propagation. First, a separated time integral scheme is built, in which time difference is divided into two separated time steps: one balances the change of the geometric discretization caused by crack growing, and the other balances the dynamic loading. Second, an adaptive energy conservation strategy is proposed for the CDCA that includes the change in the degree of nodal freedom for the crack tip element, and a new strategy for the inheritance of the degrees of nodal freedom is proposed. This method retains the enrichment scheme for the discontinuity, and the Shepard interpolation method is employed to transform the variables' values, so as to keeps the energy conservation caused by crack tip location change. Then, the enriched degree of nodal freedom values are easily passed from the crack tip enrichment to the penetrated enrichment and crack tip local coordinate system changing with crack growing. Third, a dynamic crack propagation criterion is developed, which can be used for tensile fractures and compression shear fractures. Based on those theories, a new cellular automaton model is built for dynamic crack propagation. Compared to the extended finite element method (XFEM), the calculation efficiency has been greatly improved, and several numerical examples are given to illustrate accuracy and efficiency of the present method.