Failure of classical elasticity in auxetic foams

Poisson's ratio, ν, was measured for four materials, a rubbery polymer, a conventional soft foam, and two auxetic foams. We find that for the first two materials, having ν ≥ 0.2, the experimental determinations of Poisson's ratio are in good agreement with values calculated from the shear and tensile moduli using the equations of classical elasticity. However, for the two auxetic materials (ν < 0), the equations of classical elasticity give values significantly different from the measured ν. We offer an interpretation of these results based on a recently published analysis of the bounds on Poisson's ratio for classical elasticity to be applicable.