2D and 3D cubic monocrystalline and polycrystalline materials: their stability and mechanical properties

TL;DR

This paper analyzes the mechanical stability and properties of 2D and 3D cubic monocrystalline and polycrystalline materials, focusing on their elastic moduli, Poisson's ratio, and auxetic behavior, using eigenvalue-based expressions.

Contribution

It introduces eigenvalue-based formulas for elastic moduli and Poisson's ratio, and compares auxetic regions in monocrystalline and polycrystalline cubic materials.

Findings

Polycrystalline phases have larger auxetic regions than monocrystalline ones.

Lines of zero Poisson's ratio are identified in high-symmetry directions.

Expressions for elastic properties are formulated in terms of stiffness tensor eigenvalues.

Abstract

We consider 2- and 3-dimensional cubic monocrystalline and polycrystalline materials. Expressions for Young's and shear moduli and Poisson's ratio are expressed in terms of eigenvalues of the stiffness tensor. Such a form is well suited for studying properties of these mechanical characteristics on sides of the stability triangles. For crystalline high-symmetry directions lines of vanishing Poisson's ratio are found. These lines demarcate regions of the stability triangle into areas of various auxeticity properties. The simplest model of polycrystalline 2D and 3D cubic materials is considered. In polycrystalline phases the region of complete auxetics is larger than for monocrystalline materials.