An auxetic material is one with a negative Poisson's ratio and has the property of widening when stretched or narrowing when compressed in contrast to conventional materials. Typical auxetic materials include modified polymeric foams (Lakes, 1987), regular honeycombs, polypropylene fibres and certain crystal structures. Auxetic materials benefit from enhanced mechanical properties. These benefits include improved indentation resistance, enhanced shear moduli and fracture toughness Evans and Alderson (2000).
While modelling granular materials, Bathurst and Rothenburg (1988a,b) noted the theoretical possibility of a negative Poisson's ratio if the constitutive grains had unconventional interactive properties. These unconventional interactive properties are that the tangential interaction should be stiffer than the normal interaction. In this work, a 2D unit cell has been designed with just such an unconventional interaction so that a 2D granular material can be constructed with negative Poisson's ratio. Theoretical calculations of such a granular assembly are made using mean strain assumptions and first order heterogeneity calculations. These are compared to 2D discrete element simulations, finite element simulations and Bathurst and Rothenburg's original result.