Abstract Poisson's ratio ν is defined by two orthogonal directions, one for longitudinal stretch and one for lateral strain. In elastic solids with cubic symmetry there are only two stretch directions for which ν is independent of the strain direction. All other values of ν in cubic materials can be expressed in terms of these two, ν001 and ν111, which are both restricted to the isotropic limits of −1 and 12. Extreme values of ν, which by definition lie outside the isotropic limits, occur in materials with ν001 close to 12, with the most extreme values in materials with ν111 far from 12. Simple approximate but accurate expressions for the mininum and maximum values of ν are given in terms of ν001 and ν111. Examples of materials with extreme Poisson's ratios are presented using more than 4,000 cubic materials from the Materials Project database.
Seetharaman et al. (2026) studied this question.