Poisson's ratio in cubic materials

TL;DR

This paper derives expressions for the extremal Poisson's ratio in cubic materials, revealing conditions for values less than -1 and identifying directions with large | u|, with applications to cubic crystal data.

Contribution

It provides new formulas for maximum and minimum Poisson's ratio in cubic materials and analyzes their implications for crystal data.

Findings

Poisson's ratio less than -1 occurs under specific shear modulus conditions.

Large | u| values are found near directions where Young's modulus is half of its 111 value.

Certain Indium Thallium alloys exhibit Poisson's ratio outside typical bounds.

Abstract

Expressions are given for the maximum and minimum values of Poisson's ratio $\nu$ for materials with cubic symmetry. Values less than -1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of $|\nu|$ occur in directions at which the Young's modulus is approximately equal to one half of its 111 value. Such directions, by their nature, are very close to 111. Application to data for cubic crystals indicates that certain Indium Thallium alloys simultaneously exhibit Poisson's ratio less than -1 and greater than +2.