Auxeticity of cubic materials

Abstract

AbstractA general expression for the directionally anisotropic Poisson's ratio (PR) of cubic materials under external pressure is discussed. It is expressed in terms of the elastic moduli ratios, X = G/K, Y = G/W, where K is the bulk modulus and G, W are shear moduli, and where the mechanical stability criteria are taken into account. The global maximum and global minimum PR surfaces are shown. In the X, Y‐plane, regions of different auxetic behavior are identified, and a straightforward way of classifying any cubic material as auxetic, nonauxetic, and completely auxetic is given. The domains of the different extreme directions, for which the PR shows either a global maximum or a global minimum for given X, Y, are identified and discussed. There are three extreme directions: [100], [110], and a novel, noncrystallographic one denoted as the V3‐direction. The main features of the V3 extreme direction and corresponding XY‐regions are described. It is found that the most extreme PR values can be achieved exclusively in the very limited domain of the X, Y‐plane, corresponding to the V3‐direction, and for X, Y → 0, the absolute value of the PR becomes unbounded. Analysis of literature data on real materials demonstrates that the great majority of cubic materials are nonauxetics or auxetics (with the [110] extreme direction). The materials possessing very large (i.e., PR > 2) and very small (i.e., PR < −1) PR values are identified.