Failure of classical elasticity in auxetic foams

TL;DR

This paper experimentally verifies that classical elasticity theory is invalid for materials with Poisson's ratio below 0.2, especially auxetic foams, confirming the theoretical lower bound of 0.2 for v.

Contribution

It provides direct measurements of Poisson's ratio for auxetic materials, confirming the theoretical lower limit of 0.2 for classical elasticity validity.

Findings

Measured Poisson's ratios match classical calculations for non-auxetic materials.

Classical elasticity fails to accurately predict v for auxetic materials with v < 0.

Experimental results support the theoretical lower bound of 0.2 for Poisson's ratio.

Abstract

A recent derivation [P.H. Mott and C.M. Roland, Phys. Rev. B 80, 132104 (2009).] of the bounds on Poisson's ratio, v, for linearly elastic materials showed that the conventional lower limit, -1, is wrong, and that v cannot be less than 0.2 for classical elasticity to be valid. This is a significant result, since it is precisely for materials having small values of v that direct measurements are not feasible, so that v must be calculated from other elastic constants. Herein we measure directly Poisson's ratio for four materials, two for which the more restrictive bounds on v apply, and two having values below this limit of 0.2. We find that while the measured v for the former are equivalent to values calculated from the shear and tensile moduli, for two auxetic materials (v < 0), the equations of classical elasticity give inaccurate values of v. This is experimental corroboration that the correct lower limit on Poisson's ratio is 0.2 in order for classical elasticity to apply.