Takashi Matsushima, Raphael Blumenfeld
Understanding the dependence of the structure of granular materials on grain parameters is key to predictive modelling of granular matter. Structural characteristics are commonly believed to be sensitive, for a given packing process, to intergranular friction, particle size distribution and initial conditions. We show here that the intergranular friction coefficient and the initial conditions are details, which can be scaled away, and that structures are determined mainly by the packing dynamics and the grain size distribution. This we do using the quadron description to analyse the structures of a number of numerically-generated planar disc packs in mechanical equilibrium, varying all these parameters. Our findings are as follows. 1. The mean coordination number is a universal function of the packing fraction, independent of the initial conditions, intergranular friction and size distribution we used, when "rattlers" are ignored. 2. For a given packing process and disc size distribution, both the total and conditional quadron volume distributions collapse to universal forms, independent of the initial conditions and intergranular friction. 3. The cell order distribution collapses to a universal form for all friction coefficients, initial conditions and for the two disc size distributions we studied. These results suggest that mechanically stable granular structures are determined mainly by the packing dynamics and the grains size / shape distributions - the effects of the intergranular friction and initial state can be scaled away and are therefore predictable.
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http://arxiv.org/abs/1305.6093
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