Anisotropic properties of mechanical characteristics and auxeticity of cubic crystalline media

Explicit expressions for inverse of Young's modulus E(n), inverse of shear modulus G(n, m), and Poisson's ratio v(n, m) for cubic media are considered. All these characteristics of elastic media depend on components S-11, S-12 and S-44 of the compliance tensor S, and on direction cosines of mutually perpendicular vectors n and m 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 of the stability triangle 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 v established by Hayes and Shuvalov are confirmed. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.