A general and fast convolution-based method for peridynamics: Applications to elasticity and brittle fracture

Abstract

A general and fast convolution-based method (FCBM) for peridynamics (PD) is introduced. Expressing the PD integrals in terms of convolutions and computing them by Fast Fourier Transform (FFT), the computational complexity of PD models drops from O(N2) to O(Nlog2N), with N being the number of discretization nodes. Initial neighbor identification and storing neighbor information is not required, and this means memory allocation scales with O(N) instead of O(N2), common for existing methods. FCBM is applicable to bounded domains with arbitrary shapes and boundary conditions via an “embedded constraint” (EC) approach. The formulation is shown for certain bond-based and state-based, linear and nonlinear, PD models of elasticity and dynamic brittle fracture, as applications. The method is verified on a 3D elastostatic problem and it is shown that the FCBM-PD reduces the computational time from days to hours and from years to days, compared with the original meshfree discretization for PD models. Large-scale computations of PD models are feasible with the new method, and its versatility is demonstrated by simulating, with ease, the difficult problem of cascading crack branching in a brittle plate.