Limits to Poisson’s ratio in isotropic materials

A long-standing question is why Poisson's ratio nearly always exceeds 0. 2 for isotropic materials, whereas classical elasticity predicts to be between -1 to 12. We show that the roots of quadratic relations from classical elasticity divide into three possible ranges: -1<0, 015, and 15<12. Since elastic properties are unique there can be only one valid set of roots, which must be 15<12 for consistency with the behavior of real materials. Materials with Poisson's ratio outside of this range are rare, and tend to be either very hard (e. g. , diamond, beryllium etc. ) or porous (e. g. , auxetic foams) ; such substances have more complex behavior than can be described by classical elasticity. Thus, classical elasticity is inapplicable whenever <15, and the use of the equations from classical elasticity for such materials is inappropriate.