Auxeticity of cubic materials

A 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. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim