Takashi Matsushima, Raphael Blumenfeld
Macroscopic properties of granular packs are mainly determined by the micro-structure. We study the dependence of the micro-structure on inter-granular friction and initial conditions using numerical experiments. The experiments consist of isotropic compaction of 2D assemblies of polydisperse frictional discs. We analyse the statistical properties of the quadrons - the basic micro-structural elements. We focused on the dependence on the inter-granuar friction and initial state and find several significant results. (i) We derive an analytical formula for the mean quadron volume in terms of three macroscopic quantities: the mean coordination number, the packing fraction and the rattlers fraction. This makes possible to relate directly the mean coordination number, the rattler-free packing fraction and Edwards' compactivity. (ii) We derive an initial-state-independent relation between the mean coordination number and the rattler-free packing fraction and support it numerically for a range of different systems. (iii) We collapse the quadron volume distributions from all systems onto one curve and show its consistency with the statistical mechanical approach. (iv) We study a conditional quadron volumes distribution, argued to capture fundamental features of the micro-structure, and find that these also collapse onto a single curve. (v) We find that the mean quadron volume decreases with increasing inter-granular friction coefficients, an effect prominent in high order cells, and argue that this is due to an increased probability of stable irregularly-shaped cells. We test this by a herewith developed free cell model. We conclude that the micro-structural characteristics are governed mainly by the packing procedure, while effects of inter-granular friction and initial states are details that can be scaled away.
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http://arxiv.org/abs/1207.2988
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