NONLINEAR-ANALYSIS OF THE POISSON RATIO OF NEGATIVE POISSON RATIO FOAMS

This article contains an analytic study of Poisson's ratio of re-entra nt foam materials with negative Poisson's ratio. These materials get f atter when stretched and thinner when compressed. The Poisson effect i s so fundamentally important to the properties of a material that a la rge change in the value of the ratio will have significant effects on the material's mechanical performance. Isotropic foam structures with negative Poisson's ratio have been fabricated through a permanent volu metric transformation. The cells were converted from the convex polyhe dral shape of conventional foam cells to a concave or ''re-entrant'' s hape. Mechanical behavior of a re-entrant open cell foam material will differ from that of a conventional foam in ways not addressed by exis ting theoretical treatment. Poisson's ratio as a function of strain is obtained by modeling the three-dimensional unit cell as an idealized polyhedron unit cell. Poisson's ratio is predicted to approach the iso tropic limit of -1 with increasing permanent volumetric compression ra tio of idealized cells, in comparison with experimental values as smal l as -0.8.