Comment on "Anisotropic peridynamics for homogenized microstructured materials" by Vito Diana, Andrea Bacigalupo, Marco Lepidi and Luigi Gambarotta [Comput. Methods Appl. Mech. Engrg. 392 (2022) 114704]

TL;DR

This paper critically examines a recent anisotropic peridynamics model, highlighting issues with shear stiffness and symmetry assumptions, and clarifies the limits of Poisson's ratio for 2D and 3D materials.

Contribution

It provides a detailed critique of the existing model, clarifying misconceptions about symmetries and material properties in anisotropic peridynamics.

Findings

The original model can predict zero or negative shear stiffness for certain 2D materials.

Misinterpretation of 2D versus 3D symmetries affects the model's applicability.

Limits for Poisson's ratio depend on correct symmetry assumptions.

Abstract

Recently, Vito Diana, Andrea Bacigalupo, Marco Lepidi and Luigi Gambarotta proposed an anisotropic continuum-molecular model based on pair potentials for describing the linear behavior of periodic heterogeneous Cauchy materials in the framework of peridynamic theory. Unfortunately, the proposed model for an isotropic material may have zero or even negative shear stiffness and this will be the case for Silicene or Germanene, for example. In addition, 2D symmetries were confused with 3D symmetries, and hence the limits for the Poisson's ratio.