Models and auxetic characteristics of a simple cubic lattice of spherical particles

Abstract

For a simple cubic lattice of spherical particles with three translational and three rotational degrees of freedom, using the method of structural modeling, discrete, long-wavelength continuum and higher-order gradient models are developed. The higher-order gradient model of such a medium is compared with the Lame equations for cubic symmetry media. From this comparison, the relationships are established between the second-order elastic constants and the microstructure parameters of this medium such as the size of particles and the parameters of their force and torque interactions. Based on the dependences found, the relationship between Poisson’s ratios of the considered anisotropic material and its structural parameters is analyzed. It is found that, at some values of the microstructure parameters, this medium can manifest the auxetic properties.