Anisotropic properties of mechanical characteristics and auxeticity of cubic crystalline media

摘要

Explicit expressions for inverse of Young's modulus E, inverse of shearmodulus G, and Poisson's ratio for cubic media are considered. All thesecharacteristics of elastic media depend on three components of the compliancetensor S, and on direction cosines of mutually perpendicular vectors m and nwith fourfold symmetry axes. These characteristics are studied for allmechanically stable cubic materials for vectors n belonging to the irreduciblebody angle subtended by three cubic high symmetry directions [001], [111], and[110]. Regions in the stability triangle of in which cubic elastic materialsare completely auxetic, non-auxetic, and auxetic are established. Severalintermediate-valence compounds belonging to the region of complete auxecity areindicated. The extreme properties of E^{-1}, G^{-1} and Poisson ratioestablished by Hayes and Shuvalov are confirmed.