On a spring-network model and effective elastic moduli of granular materials

Two challenges in mechanics of granular media are taken up in this paper: ( i) development of adequate numerical discrete element models of topological ly disordered granular assemblies and (ii) calculation of macroscopic elast ic moduli of such materials using effective medium theories. Consideration of the first one leads to an adaptation of a spring-network (Kirkwood) mode l of solid-state physics to disordered systems, which is developed in the c ontext of planar Delaunay networks. The model! employs two linear springs: a normal one along an edge connecting two neighboring vertices (grain cente rs) which accounts for normal interactions between the grains, as well as a n angular one which accounts for angle changes between two edges incident o nto the same vertex; edges remain straight and grain rotations do not appea r This model is then used to predict elastic moduli of two-phase granular m aterials-random mixtures of soft and stiff grains-for high coordination num bers. It is found here that an effective Poisson's ratio, nu(eff), Of such a mixture is a convex function of the volume fraction, so that nu(eff) may become negative when the individual Poisson's ratios of both phases are bot h positive. Additionally, the usefulness of three effective medium theories -perfect disks, symmetric ellipses, and asymmetric ellipses-is tested.