Negative Poisson's Ratio Materials.

Reentrant polymer foam materials with negative Poisson's ratios, as described by Lakes (1), are a new class of materials with unique properties. The thermodynamic restriction on the compressibility, K, of an elastic material is that it must be positive for stability. The compressibility is related to the shear modulus, G, and Poisson's ratio, v, by K = 3/2[(1 2v)/G(1+ v)], so v is restricted to -1 < v < 1/2 for positive K, as is well known. However, polymer foams are not elastic continua and develop couplemoment stresses that bend the internal connecting ligaments. The negative values of v in the reentrant foams are a direct result of the size scale, intrinsic in couple-moment elastic theory. Thus there are hidden variables in the material. Anisotropic materials with matrix elastic constants have some negative Poisson's ratios. These materials also have additional hidden variables-the complete set of tensorial, stress-strain, state variables. Although a proof does not exist that restricts the ratio of transverse-to-lateral strains to a value that is larger than zero, for a system of two independent variables, that is, two stresses and two strains, Lakes' observations should not be construed as evidence that such a proof is impossible. His material has additional hidden state variables. All known continuum solids that are described by two independent-state variables have thermodynamic couplings that are greater than zero. The proof that this must be true has simply eluded us. STEPHEN BuRNs Materials Science Program, Department ofMechanical Engineering, University ofRochester, Rochester, NY 14627