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A long-standing question is why Poisson's ratio v nearly always exceeds 0.2for isotropic materials, whereas classical elasticity predicts v to be between-1 to 1/2. We show that the roots of quadratic relations from classicalelasticity divide v into three possible ranges: -1 < v <= 0, 0 <= v <= 1/5, and1/5 <= v < 1/2. Since elastic properties are unique there can be only one validset of roots, which must be 1/5 <= v < 1/2 for consistency with the behavior ofreal materials. Materials with Poisson's ratio outside of this range are rare,and tend to be either very hard (e.g., diamond, beryllium) or porous (e.g.,auxetic foams); such substances have more complex behavior than can bedescribed by classical elasticity. Thus, classical elasticity is inapplicablewhenever v < 1/5, and the use of the equations from classical elasticity forsuch materials is inappropriate.

Limits to Poisson's ratio in isotropic materials