Modelling and testing of a foldable macrostructure exhibiting auxetic behaviour

Auxetics exhibit the anomalous property of getting fatter Auxetics than thinner when uniaxially stretched [negative Poisson's ratio (NPR)]. This paper presents an analytical model of a structure constructed from umbrella type sub-units which is predicted to exhibit this property together with the results of mechanical tests of a structure having this geometry. It is shown that such systems can exhibit negative on-axis Poisson's ratio of -1 which means that they maintain their aspect ratio, while Poisson's ratio becomes less negative for loading off-axis. It is also shown that this model can explain the sign and anisotropy of Poisson's ratio demonstrated by a molecular level system constructed from calix(4)arenes having the same geometry.