Failure of Classical Elasticity in Auxetic Foams

The lower bound customarily cited for Poisson’s ratio ν is −1, which was derived from the relationship between the bulk and shear moduli in classical elasticity. To test this theory, we measured ν for four materials, a polymeric rubber, 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 equations of classical elasticity. However, for the auxetic foams (ν < 0), classical elasticity give values significantly different from the measured ν. We review how the customary lower bound for ν was derived, present a new analysis which demonstrates that the lower limit for ν is 1/5, and show how these results are consistent with this new analysis.