Parametric identification of crystals having a cubic lattice with negative Poisson's ratios

A two-dimensional model of an anisotropic crystalline material with cubic symmetry is considered. This model consists of a square lattice of round rigid particles, each possessing two translational and one rotational degree of freedom. Differential equations that describe propagation of elastic and rotational waves in such a medium are derived. A relationship between three groups of parameters is found: second-order elastic constants, acoustic wave velocities, and microstructure parameters. Values of the microstructure parameters of the considered anisotropic material at which its Poisson's ratios become negative are found.