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

TL;DR

This paper presents a fast convolution-based method for peridynamics that significantly reduces computational complexity and memory usage, enabling large-scale simulations of elasticity and brittle fracture with arbitrary domain shapes.

Contribution

The paper introduces FCBM, a convolution-based approach using FFT to efficiently compute peridynamics models without neighbor search, applicable to complex geometries and boundary conditions.

Findings

Reduces computational time from days to hours for 3D elastostatic problems.

Decreases memory requirements from O(N^2) to O(N).

Successfully simulates complex crack branching in brittle materials.

Abstract

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