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Geometric shape is an important factor that affects the packing and mechanical properties of granular material. In this paper, we use four families of assembled rods to model an entangled material in simulations. The particles are all non-convex and have the ability to interpenetrate. Together with elongation, central symmetry, which is attributed to the intersection location of the elementary rods, is also a main factor that produces varieties of particle shapes. With a certain total elongation, the dense disordered packing density is verified to be independent of the elongation distribution of the elementary rods. The specific shape hardly affects the packing densities. Therefore, the empirical formula to predict the packing density is extended to apply to all assembled rods with any elongation distribution. Different from the packing density, the shape disparity caused by central symmetry is found to significantly influence the contacts between neighboring particles. Due to more multipoint contacts contributing more constraints around the central particle, the centrally symmetric 3DX-shaped particles can more easily interpenetrate in the granular system. Moreover, the higher number of constraints contributed by neighboring contacts reflects the hyperstaticity of packings, which suggests mechanical stability for disordered packings of non-convex assembled rods. • Effects of central symmetry and elongation have been studied via simulations. • An empirical formula to predict the packing density has been proposed. • Central symmetry is verified to make effect on contacts in the granular system. [ABSTRACT FROM AUTHOR]

The packing of rod-like particles, which is common in physical and mathematical studies, has arisen in a variety of industrial applications. Elongation effect on the packing properties of rod-like particle has been well investigated. Besides that, rod-like particles can be easily deformed into a large amount of non-convex shapes by simply bending or assembling several particles, in which effects of non-convex deformations should also be concerned. In this work, the packing behaviors of particulate systems composed of various non-convex deformations of rod-like particles are numerically simulated via the analytical model and the relaxation algorithm. The packing configurations are further optimized using the Monte Carlo method to eliminate the local ordered structures. 8 shapes of non-convex particles including 2-dimensional and 3-dimensional particles are employed in the packing systems. Independent of aspect ratio, the dense random packing densities of identical assembled rods are up to 20% higher than those of spherocylinders and are less dependent from the specific particle shape. However, the coordination numbers of various non-convex particle packings are quite different. With a parameter of convex ratio defined, a packing composed of more non-convex particles will have a higher coordination number. This indicates that for more non-convex particle packings, there are more constraints and entanglements among neighboring particles, resulting in a more stable configuration. The nearest-neighbor contact to a centered particle in 3DX-shaped particle packings is quite different from those of other shapes, which can be identified from the location of the first peak in the radial distribution function. It is also the cause to the distinct disparities of estimated excluded volumes of non-convex particles simulated in this work. [ABSTRACT FROM AUTHOR]

We apply the ideal octahedron model and the relaxation algorithm in generating octahedron packings. The cubatic order parameter [ P 4 ] 1 , bond-orientational order metric Q 6 , and local cubatic order parameter P 4 l o c a l of the packings are calculated and their correlations with the packing density are investigated in the order maps. The border curve of packing density separates the geometrically feasible and infeasible regions in the order maps. Observing the transition phenomenon on the border curve, we propose the concept of the maximally dense random packing (MDRP) as the densest packing in the random state in which the particle positions and orientations are randomly distributed and there is no nontrivial spatial correlations among particles. The MDRP characterizes the onset of nontrivial spatial correlations among particles. A special packing with a density about 0.7 is found in the order maps and considered to be the MDRP of octahedra. The P 4 l o c a l is proposed as a new order parameter for octahedron packings, which measures the average order degree in the neighborhoods of particles. The [ P 4 ] 1 , Q 6 and P 4 l o c a l evaluate the order degree of orientation, bond orientation and local structures, respectively and are applied simultaneously to measure the order degree of the octahedron packings. Their thresholds in the random state are determined by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]