The mathematical model for anisotropic material with auxetic properties

A two-dimensional model representing a square lattice of round particles is proposed for description of auxetic properties of an anisotropic crystalline material with cubic symmetry. It is assumed that each particle has two translational and one rotational degrees of freedom. Differential equations describing the propagation of elastic and rotational waves in such a medium have been derived. Relationships between the macroelasticity constants of the medium and the parameters of its inner structure have been found. It has been shown that the Poisson's ratios of the anisotropic material can be negative for certain values of the parameters of its inner structure.