Micromechanical simulation and analysis of one-dimensional vibratory sphere packing

Bimodal self-assembly of granular spheres under vertical vibration

As granular particles in a packing are athermal, their self-assembly has to be realized with the input of energy via walls. But different manners of energy input, e.g., through tapping or shearing walls, have not been discriminated previously. We address this problem in the self-assembly of identical granular spheres in prism-like containers subjected to one-dimensional (1D) vertical vibration by numerical simulations. The edge lengths or diameter of the containers are the integer multiples of the particle diameter. When energy is input with the vibration, the particles can self-assemble into mainly mixed FCC (face-centred-cubic) and HCP (hexagonal-close-packed) structures from the bottom wall and/or the side walls. According to different movements of the walls, the shear-induced and tap-induced self-assemblies are distinguished. These two self-assembly modes can emerge solely or simultaneously, with different but overlapping regions in the vibration amplitude and frequency phase diagram. The structures of the self-assembly from the two modes also present different features, suggesting different formation mechanisms. Moreover, it is found that the close-packed planes of the ordered clusters formed from different walls are often misaligned, leading to conflicts in the self-assembly of the whole system. These findings are helpful for both the understanding and controlling of the self-assembly of granular particles and other similar athermal and low-thermal systems.

Self-assembly of granular spheres under one-dimensional vibration

The self-assembly of uniform granular spheres is related to the fundamentals of granular matter such as the transitions of phases, order/disorder and jamming states. This paper presents a DEM (discrete element method) study of the continuous self-assembly of uniform granular spheres from random close packing (RCP) to partially and nearly fully ordered packings under one-dimensional (1D) sinusoidal vibration without other interventions. The effects of the vibration amplitude and frequency are investigated in a wide range. The structures of the packings are characterized in terms of packing fraction and other microscopic structural parameters, including the coordination number, bond-orientational orders, and, in particular, ordered clusters, by adaptive common neighbor analysis (a-CNA). It is shown that 1D vibrations can also lead to the self-assembly of uniform granular spheres with packing fractions exceeding the RCP limit, and FCC (face centered cubic) and HCP (hexagonal close packed) structures coexist in the self-assembled packings while their total fraction can reach nearly 100%. The structures of these packings can be better correlated with the vibration velocity amplitude rather than the commonly used vibration intensity. The dynamics of such self-assembly is also preliminarily analyzed. Our study not only presents the conditions for the self-assembly of uniform granular spheres under 1D vibration, but also characterizes the order-disorder transitions during the process, which can improve our understanding of the fundamentals of granular materials and jamming states.

Dynamic modelling on the confined crystallization of mono-sized cubic particles under mechanical vibration

The dynamic crystallization of cubic granular particles under three-dimensional mechanical vibration is numerically investigated by the discrete element method. The effects of operational conditions (vibration, container shape and system size) and particle properties (gravity and friction) on the formation of crystals and defects are discussed. The results show that the formation and growth of clusters with face-to-face aligned cubic particles can be easily realized under vibrations. Especially, a single crystal with both translational and orientational ordering can be reproduced in a rectangular container under appropriate vibrations. It is also found that the gravitational effect is beneficial for the ordering of a packing; the ordering of frictional particles can be improved significantly with an enlarged gravitational acceleration. The flat walls of a rectangular container facilitate the formation of orderly layered structures. The curved walls of a cylindrical container contribute to the formation of ring-like structures, whereas they also cause distortions and defects in the packing centers. Finally, it is shown that the crystallization of inelastic particles is basically accomplished by the pursuit of a better mechanical stability of the system, with decreasing kinetic and potential energies.

Local rotational symmetry in the packing of uniform spheres

Local rotational symmetry (LRS) of a particulate system is important for understanding its structure and phase transition. However, how to properly characterize LRS for this system is still a challenge as the system normally includes both ordered and disordered local structures. Herein, based on the so-called common neighbour subcluster (CNS), we proposed a method to characterize the LRS of uniform spheres packings with the packing fraction ρ ranging within 0.20 and 0.74. It was found that different fold LRSs coexist in most packings, and their maximum degree increases at ρ < 0.64, except for the 2-fold LRS held by 6-sphere CNS that continuously increases to form the fcc crystal at ρ = 0.74. The overall LRS involving all the CNSs monotonically increases with two critical changes at ρ = (0.35-0.40) and 0.64; the evolution of individual LRSs held by specific CNS groups critically changes at ρ ≈ (0.35-0.40), 0.50, 0.55-0.60, and 0.64. The physics corresponding to these critical changes has also been discussed. The findings will significantly enrich the understanding of the structural symmetry of materials including atoms and particles.

Structural characterization of the packings of granular regular polygons

By using a recently developed method for discrete modeling of nonspherical particles, we simulate the random packings of granular regular polygons with three to 11 edges under gravity. The effects of shape and friction on the packing structures are investigated by various structural parameters, including packing fraction, the radial distribution function, coordination number, Voronoi tessellation, and bond-orientational order. We find that packing fraction is generally higher for geometrically nonfrustrated regular polygons, and can be increased by the increase of edge number and decrease of friction. The changes of packing fraction are linked with those of the microstructures, such as the variations of the translational and orientational orders and local configurations. In particular, the free areas of Voronoi tessellations (which are related to local packing fractions) can be described by log-normal distributions for all polygons. The quantitative analyses establish a clearer picture for the packings of regular polygons.

Radical tessellation of the packing of spheres with a log-normal size distribution

The packing of particles with a log-normal size distribution is studied by means of the discrete element method. The packing structures are analyzed in terms of the topological properties such as the number of faces per radical polyhedron and the number of edges per face, and the metric properties such as the perimeter and area per face and the perimeter, area, and volume per radical polyhedron, obtained from the radical tessellation. The effect of the geometric standard deviation in the log-normal distribution on these properties is quantified. It is shown that when the size distribution gets wider, the packing becomes denser; thus the radical tessellation of a particle has decreased topological and metric properties. The quantitative relationships obtained should be useful in the modeling and analysis of structural properties such as effective thermal conductivity and permeability.