Discrete Micromodulus Functions for Reducing Wave Dispersion in Linearized Peridynamics

Abstract

Typical implementations of peridynamics use a constant or tapered micromodulus (or influence) function, the choice of which has been shown to have a large impact on the dispersion relation. In this work, a method for computing micromodulus function values at discretized points within a node’s horizon is presented for linearized peridynamics. The technique involves constructing a system of equations representing the desired dispersion relation and solving for the micromodulus function coefficients at discretized node locations. Both 1D and 2D formulations are presented. A straightforward implementation of the method results in negative coefficients, which improve wave propagation accuracy, but results in unstable solutions of fracture problems using a bond-breakage scheme. Two methods for addressing this issue are discussed: A hybrid method that uses a constant micromodulus function after damage has occurred at a node, and a constrained solution that results in only positive coefficients. The dispersion properties of the method are examined in detail, including the numerical anisotropy in 2D. Finally, results for wave propagation in 1D and 2D, static fracture, and dynamic fracture are given.