Numerical simulation of dynamic fractures in 2D FGMs using the numerical manifold method

Abstract

In this study, the numerical manifold method is used with an explicit time integration scheme to implement dynamic fracture analysis of 2D functionally graded materials. The framework of the numerical manifold method is used to discretize the dynamic equilibrium equation in the spatial domain. Instead of the commonly used Newmark method, the precise time step integration method is used for temporal discretization, and the detailed implementations of the proposed technique are described in detail in this paper. The dynamic stress intensity factors that can describe the inertia effect are extracted by the domain form of the interaction integral with nonequilibrium formulation. For verification purposes, four numerical examples with increasing complexity are investigated, in which different material gradients, crack configurations and loading forms are considered. Simulation results show that the proposed method achieves high reliability and precision for dynamic problems of 2D cracked functionally graded materials.