No abstract

We present a systematic investigation of the morphology and space-filling properties of polydisperse densely packed granular media in two dimensions. A numerical procedure is introduced to generate collections of circular particles with size distributions of variable shape and span constrained by explicit criteria of statistical representativity. We characterize the domain of statistically accessible distribution parameters for a bounded number of particles. This particle generation procedure is used with two different deposition protocols in order to build large close-packed samples of prescribed polydispersity. We find that the solid fraction is a strongly nonlinear function of the size span, and the highest levels of solid fraction occur for the uniform distribution by volume fractions. As the span is increased, a transition occurs from a regime of topological disorder where the packing properties are governed by particle connectivity to a regime of metric disorder where pore-filling small particles prevail. The polydispersity manifests itself in the first regime through the variability of local coordination numbers. We observe a continuous decrease of the number of particles with four contacts and the growth of two populations of particles with three and five contacts. In the second regime, radial distribution functions show that the material is homogeneous beyond only a few average particle diameters. We also show that the packing orientational order is linked with fabric anisotropy and it declines with size span.

By means of contact dynamics simulations, we investigate the shear strength and internal structure of granular materials composed of two-dimensional nonconvex aggregates. We find that the packing fraction first grows as the nonconvexity is increased but declines at higher nonconvexity. This unmonotonic dependence reflects the competing effects of pore size reduction between convex borders of aggregates and gain in porosity at the nonconvex borders that are captured in a simple model fitting nicely the simulation data both in the isotropic and sheared packings. On the other hand, the internal angle of friction increases linearly with nonconvexity and saturates to a value independent of nonconvexity. We show that fabric anisotropy, force anisotropy, and friction mobilization, all enhanced by multiple contacts between aggregates, govern the observed increase of shear strength and its saturation with increasing nonconvexity. The main effect of interlocking is to dislocate frictional dissipation from the locked double and triple contacts between aggregates to the simple contacts between clusters of aggregates. This self-organization of particle motions allows the packing to keep a constant shear strength at high nonconvexity.