The continuous-discontinuous cellular automaton method for elastodynamic crack problems

In this paper, the recently proposed continuous-discontinuous cellular automaton method (CDCA) is further developed for elastodynamic problems in 2D elastic solids. A continuity-to-discontinuity enriched function technique is developed for elastodynamics and combined with a cellular automaton formulation; the cellular automaton theory for elastodynamics, in which fast adaptive updating rules for the cell and its neighbors are developed, and the time domain CDCA are proposed. In this method, the cracks are independent of the integral meshes, and no assembled global matrix is needed for the whole process. Time-dependent equations for the cells are discretized by the Newmark method, and rapidly solved by the cellular automaton method. To analyze the fracture behaviors of elastic solids with dynamic loads, mixed-mode dynamic stress intensity factors are obtained by the interaction integral method. Some numerical examples for elastodynamic problems are studied to validate the accuracy and efficiency of the present method, and solutions from analytical method and some other methods are employed to show the high accuracy of the CDCA.