Anisotropic properties of mechanical characteristics and auxeticity of cubic crystalline media

TL;DR

This paper derives explicit formulas for elastic properties of cubic crystalline media, analyzing their anisotropic and auxetic behavior across different directions and stability regions, confirming extreme property bounds.

Contribution

It provides explicit expressions for elastic moduli and Poisson's ratio in cubic media, mapping auxetic and non-auxetic regions in the stability triangle.

Findings

Identified regions of complete auxeticity in cubic materials.

Confirmed extreme bounds of elastic properties by Hayes and Shuvalov.

Mapped directional dependence of elastic characteristics in cubic crystals.

Abstract

Explicit expressions for inverse of Young's modulus E, inverse of shear modulus G, and Poisson's ratio for cubic media are considered. All these characteristics of elastic media depend on three components of the compliance tensor S, and on direction cosines of mutually perpendicular vectors m and n with fourfold symmetry axes. These characteristics are studied for all mechanically stable cubic materials for vectors n belonging to the irreducible body angle subtended by three cubic high symmetry directions [001], [111], and [110]. Regions in the stability triangle of in which cubic elastic materials are completely auxetic, non-auxetic, and auxetic are established. Several intermediate-valence compounds belonging to the region of complete auxecity are indicated. The extreme properties of E^{-1}, G^{-1} and Poisson ratio established by Hayes and Shuvalov are confirmed.