A long-standing question is why Poisson's ratio ν nearly always exceeds 0.2 for isotropic
materials, whereas classical elasticity predicts ν to be between− 1 to 1 2. We show that the
roots of quadratic relations from classical elasticity divide ν into three possible ranges:− 1<
ν≤ 0, 0≤ ν≤ 1 5, and 1 5≤ ν< 1 2. Since elastic properties are unique there can be only
one valid set of roots, which must be 1 5≤ ν< 1 2 for consistency with the behavior of real
materials. Materials with Poisson's ratio outside of this range are rare, and tend to be either …

The lower bound customarily cited for Poisson's ratio ν,− 1, is derived from the relationship
between ν and the bulk and shear moduli in the classical theory of linear elasticity. However,
experimental verification of the theory has been limited to materials having ν⩾ 0.2. From
consideration of the longitudinal and biaxial moduli, we recently determined that the lower
bound on ν for isotropic materials from this theory is actually $\frac {1}{5} $. Herein we
generalize this result, first by analyzing expressions for ν in terms of six common elastic …