Negative Poisson's ratio materials' design principles and possible applications

We propose 2D and 3D structures possessing macroscopic negative Poisson’s ratio. The approach is based on considering a granulate material with stiff shear and soft normal stiffnesses of contacts. Homogenisation by differential expansion is used to determine the effective (macroscopic) moduli. We also study hybrid materials consisting of positive and negative Poisson’s ratio components. We show that multiscale distribution of negative Poisson’s ratio inclusions of various shapes in a positive Poisson’s ratio elastic isotropic matrix considerably increases the effective Young’s modulus even when the Young’s moduli of the matrix and inclusions are the same.