A General Numerical Method to Model Anisotropy in Discretized Bond-Based Peridynamics

TL;DR

This paper introduces a versatile numerical approach to determine bond micromoduli in anisotropic bond-based peridynamics, enabling accurate reproduction of anisotropic stiffness tensors for various material symmetries.

Contribution

It presents a least-squares based numerical method to find bond micromoduli that exactly match anisotropic stiffness tensors, including all elastic symmetries, under certain conditions.

Findings

Method accurately reproduces anisotropic stiffness tensors.

Robustness demonstrated across various parameters and symmetries.

Solution aligns with classical elasticity in example cases.

Abstract

This work proposes a novel, general and robust method of determining bond micromoduli for anisotropic linear elastic bond-based peridynamics. The problem of finding a discrete distribution of bond micromoduli that reproduces an anisotropic peridynamic stiffness tensor is cast as a least-squares problem. The proposed numerical method is able to find a distribution of bond micromoduli that is able to exactly reproduce a desired anisotropic stiffness tensor provided conditions of Cauchy's relations are met. Examples of all eight possible elastic material symmetries, from triclinic to isotropic are given and discussed in depth. Parametric studies are conducted to demonstrate that the numerical method is robust enough to handle a variety of horizon sizes, neighborhood shapes, influence functions and lattice rotation effects. Finally, an example problem is presented to demonstrate that the proposed method is physically sound and that the solution agrees with the analytical solution from classical elasticity. The proposed method has great potential for modeling of deformation and fracture in anisotropic materials with bond-based peridynamics.