Normal and shear behaviours of the auxetic metamaterials: homogenisation and experimental approaches

The auxetic metamaterials exhibit attractive mechanical properties, including negative Poisson’s ratio and compressional resistance. Although auxetic metamaterials have been extensively investigated using experimental and computational approaches, the consistent estimation of shear properties has still not been clarified. According to Cauchy elasticity, the shear properties of an auxetic structure should be enhanced owing to the negative Poisson’s ratio. However, this study used homogenisation and experimental approaches to demonstrate that the shear elasticity is highly non-linear with respect to the characteristic geometrical parameters of a unit cell and that shear properties, particularly normal elasticity, are not always improved. Furthermore, the estimation of the shear elasticity based on the classical isotropic continuum elasticity relations can result in misleading values and should be avoided.