Nonlinear Analysis of the Poisson's Ratio of Negative Poisson's Ratio Foams

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Abstract
This article contains an analytic study of Poisson's ratio of re-entrant foam materials with negative Poisson's ratio. These materials get fatter when stretched and thinner when compressed. The Poisson effect is so fundamentally important to the properties of a material that a large 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 volumetric transformation. The cells were converted from the convex polyhedral shape of conventional foam cells to a concave or "reentrant" shape. Mechanical behavior of a re-entrant open cell foam material will differ from that of a conventional foam in ways not addressed by existing 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 isotropic limit of −1 with increasing permanent volumetric compression ratio of idealized cells, in comparison with experimental values as small as −0.8.

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