Cubic materials in different auxetic regions: Linking microscopic to macroscopic formulations

A number of basic features of the mechanical properties of a cubic symmetry solid material are identified and discussed within the framework of the XY-plane approach, where X?=?G/K, Y?=?G/W, K is the bulk modulus and G, W are shear moduli. An anisotropic part of the Debye temperature is analysed, which was found to be weakly dependent on X and is mainly determined by Y which quantifies the material elastic anisotropy. The anisotropic part has a considerable effect on the Debye temperature of partially auxetic materials. An empirical ductility-brittleness criterion is considered, which indicates that many auxetics may deform in a brittle manner. A possible correlation between directional tensile deformation and the surface of the most extreme Poisson's ratio (PR) values is suggested. Finally, the reasons for the paucity of cubic materials in the part of the XY-plane with low Y values is investigated using static microscopic models in which the particles interact with nearest and next nearest neighbours only. An example of a type of microscopic model system located in this empty region has been found, which consists of a system under tension, where the interparticle interaction decays with distance in an oscillatory way. The results obtained suggest that a rather unconventional form of the interparticle interaction set and thermodynamic conditions may therefore be required to develop a solid material with these mechanical properties.