Auxetic behaviour and anisotropic heterogeneity

To date, microstructural modelling of auxetic materials has relied mainly on the assumption of both a regular and a homogeneous microstructure present throughout the bulk material. The disorder within a material is seen as something undesirable, with the expectation that disorder or heterogeneity will tend to reduce the range of properties available. In this work the presence of short-range variations in the elastic moduli are considered together with the resulting effect on a material’s Poisson’s ratio. It is shown that such variations alone can cause a material with a mean positive Poisson’s ratio to become negative (auxetic). In addition, anisotropic variations can enhance the magnitude of a negative Poisson’s ratio.