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Abstract
The packing of granular materials is a basic and important problem in geomechanics. An approach, which generates dense packing of spheres confined in cylindrical and cuboidal containers in three steps, is introduced in this work. A loose packing structure is first generated by means of a reference lattice method. Then a dense packing structure is obtained in a container by simulating dropping of particles under gravitational forces. Furthermore, a scheme that makes the bottom boundary fluctuate up and down was applied to obtain more denser packing. The discrete element method (DEM) was employed to simulate the interactions between particle-particle and particle-boundary during the particles' motions. Finally, two cases were presented to indicate the validity of the method proposed in this work.
Highlights
The compaction of granular materials is a current subject of keen interest, which is widely used in sciences and engineering; for example, a compaction structure of granular materials can be used to model the structure of granular media, liquids, living cells, glasses, and random media
The packing fraction of equal spheres’ packing in three dimensions cannot exceed that of the face-centered cubic packing, π/√18 and this is the famous Kepler conjecture
Many methods have been developed to obtain higher density of particle packing. These methods can be divided into four types: geometric method (GM), discrete element method (DEM), combined geometry and particle motion (CGPM), and Monte Carlo method (MC)
Summary
The compaction of granular materials is a current subject of keen interest, which is widely used in sciences and engineering; for example, a compaction structure of granular materials can be used to model the structure of granular media, liquids, living cells, glasses, and random media. Many methods have been developed to obtain higher density of particle packing These methods can be divided into four types: geometric method (GM), discrete element method (DEM), combined geometry and particle motion (CGPM), and Monte Carlo method (MC). In the GM, the particles’ motions are not considered and a dense packing was formed by a purely geometrical computation; for example, Place and Mora, Delarue and Jeulin [4, 5] randomly placed a given number of particles within 3D space and a dense packing was obtained by filling the remaining voids with particles. In the CGPM, the geometrical method was used, and the particles’ motions were considered, for example, Lubachevsky and Stillinger’s compression algorithm [9,10,11], and the spheres grow in size during the process of the simulation at a certain expansion rate until a final state with diverging collision rate is reached. The bottom boundary of the container was fluctuated up and down to reach a more dense packing
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