On contact numbers in random rod packings

Abstract

Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well with experiments on granular packings. Contact numbers are also compared to caging numbers calculated for sphero-cylinders with arbitrary aspect-ratio. The caging number for rods arrested by uncorrelated point contacts asymptotes towards γ = 9 at high aspect ratio, strikingly close to the experimental contact number C ≈ 9.8 for thin rods. These and other findings confirm that thin-rod packings are dominated by local arrest in the form of truly random neighbor cages. The ideal packing law derived for random rod-rod contacts, supplemented with a calculation for the average contact number, explains both absolute value and aspect-ratio dependence of the packing density of randomly oriented thin rods.

Fire ants actively control spacing and orientation within self-assemblages

“…Through simulation, Philipse showed the contact number of packed spherocylinders asymptotically reaches c=10 as aspect ratio α is increased. The expected contact number of spherocylinders for an α matching our ants is 9 (Wouterse et al, 2009). Comparing this contact number with our measured result of 14.3 connections, it is clear that ants actively create many more connections than would be expected for equivalently shaped passive granular materials.…”

Granular materials composed of shape-anisotropic grains

“…For the case of high aspect ratio sphero-cylinders, γ was found to be around 10 in experiments [62,63,65] and numerical simulations [47] (see Fig. 3).…”

“…Isotropy of packing is another issue. A so-called mechanical contraction method (MCM) [46], and hybrid (MCM + DEM) approaches [47] have been employed. In iterative steps, particle positions in a random dilute ensemble are rescaled, subsequently overlapping particles are shifted into free volumes until the system is congested [46].…”

Particle shape effects on the stress response of granular packings

“…While it has long been recognized that particle shape plays a significant role in controlling a granular material's microstructure, [1][2][3][4][5] most work to date using three-dimensional particles has focused on spheres and a small set of anisotropic shapes, such as ellipsoids, [6][7][8][9] and rods. 10,11 Recently, progress has been made by systematically investigating the microstructural configurations of more complex shapes including faceted polyhedra, [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] often with the particular goal of finding the highest achievable packing fraction. [13][14][15]17,20,24 By contrast, the response of aggregates of non-spherical particles to applied mechanical loads has been explored much less.…”