Negative Poisson’s ratio in a transversely isotropic foam structure

Recent experimental work has shown that foams having a negative Poisson’s ratio may be fabricated by inverting the usual energetically preferred tetrahedral structure to form a reentrant structure. It is shown here that a linear elastic analysis of a two-dimensional reentrant honeycomb provides a theoretical prediction of the negative Poisson’s ratio in the plane for a transversely isotropic material. The value of Poisson’s ratio depends upon the reticulation angle, which is related to the permanent volumetric compression ratio required to form the reentrant structure.