Microstructural characteristics of planar granular solids

The microstructure of granular materials is the main factor determining their macroscopic behaviour. We study systematically the statistical characteristics of volume elements (called quadrons) of microstructures of monoand polydisperse planar disc packs granular and report a number of new results. The packs analysed were of different intergranular friction coefficients ,μ , contained about 20,000 discs each and were brought to mechanical equilibrium under identical isotropic compression stresses from three different initial states: loose, intermediate and dense. Our findings are the following. (i) The rattlers volume fraction φr is not affected by the disc size distribution (DSD). (ii) Excluding the rattlers, we find that the relation between the packing fraction φ ′ and the mean coordination number z̄ is independent of the initial state. Together with result (i), this allows us to separate the effects of the DSD and the initial state on the microstructure. (iii) We relate analytically z̄, φ ′ and the (normalised) mean quadron volume v̄′. (iv) Combining (iii) and a relation between z̄ and the mean cell order, ē, derived from Euler’s topological relation, we show that (ii) is a result of the geometrical relation between v̄′ and ē. (v) The probability density function of the quadron volumes, normalised by v̄′, is universal for all the studied systems and it can be fit reasonably well by a Γ distribution.