Contact anisotropy and coordination number for a granular assembly: A comparison of distinct-element-method simulations and theory

We study an ideal granular aggregate consisting of elastic spherical particles, isotropic in stress and anisotropic in the contact network. Because of the contact anisotropy, a confining pressure applied at zero deviatoric stress, produces shear strain as well as volume strain. Our goal is to predict the coordination number k, the average number of contacts per particle, and the magnitude of the contact anisotropy e, from knowledge of the elastic moduli of the aggregate. We do this through a theoretical model based upon the well known effective medium theory. However, rather than focusing on the moduli, we consider their ratios over the moduli of an equivalent isotropic state. We observe good agreement between numerical simulation and theory.