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

We introduce a general and fast convolution-based method (FCBM) for peridynamics (PD). Expressing the PD integrals in terms of convolutions computing them by Fourier transform (FFT), we reduce computational complexity models from O(N^2) to O(Nlog_2 N), with N being total number discretization nodes. Initial neighbor identification storing information is not required, and, as consequence, memory allocation scales O(N) instead O(N^2), common existing methods. The applicable bounded domains arbitrary shapes boundary conditions via an embedded constraint (EC) approach. explain FCBM-EC formulation certain bond-based state-based, linear nonlinear elasticity dynamic brittle fracture, applications. solve 3D elastostatic problem show that FCBM reduces time days hours years days, compared original meshfree models. Large-scale computations are feasible new method, demonstrate its versatility simulating, ease, difficult multiple crack branching plate.