Anisotropic properties of mechanical characteristics and auxeticity of cubic crystalline media

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.