A statistical analysis of void size distribution in a simulated narrowly graded packing of spheres

The void microstructure of a simulated packing of polydisperse spheres has been investigated by means of a radical Delaunay tessellation. We have focused on creating sphere packings by mimicking processes involved in the construction of embankment dams: the polydisperse spheres are collectively released under gravity and denser states are mainly obtained by means of shearing cycles. This study has been performed on a narrowly graded material for four porosities ranging from 0.42 to 0.36. The void structure is quantified in terms of probability density functions of pore and constriction sizes, cumulative distributions and connectivity functions. We emphasize the implications of the sample construction technique on the geometric packing arrangements, among them a well disordered medium where tetrahedra remain the most represented unit void structure. We point out that when porosity decreases, void distributions become narrower but the initial structure is never destroyed. Nevertheless, the densification modifies significantly the computed mean void quantities. In this study, usual geometric arrangements obtained for very dense materials are not encountered.     

On ten- and eleven-coordinated periodic packings of equivalent spheres

It is shown that ten- and eleven-coordinated packings of symmetry-equivalent spheres can be derived by a continuous deformation of closest packing. The tetragonal ten- and eleven-coordinated close packings described in the literature are special $\text{minimum}$ density, cases of these deformations.     

Simulation of the packing of granular mixtures of non-convex particles and voids characterization

The simulation of granular materials has considerably developed in the last decades essentially with simple geometry particles. The purpose of this paper is to study granular systems of non-convex particles which are present in many industrial processes. Two shapes of large and two shapes of small non-convex particles resulting from the cutting of a hollow cylinder are modelled, and binary mixtures containing varying proportions of small and large particles are generated with a Monte Carlo simulation. Two different states of the granular systems are studied: suspensions and packings obtained after sedimentation. No contact force model is used and only steric repulsion is taken into account. The density, the pore size distribution and the tortuosity of the granular systems are studied. The results are compared to those obtained with granular systems of convex particles.     

Analysis of the packing structure of wet spheres by Voronoi–Delaunay tessellation

The structure of a packing of narrowly sized wet spheres with packing density 0.435 is analysed against the well-established random close packing with packing density 0.64 by means of the Voronoi and Delaunay tessellation. The topological and metric properties of Voronoi polyhedra, such as the number of faces, perimeter, area and volume of a polyhedron, the number of edges, perimeter and area of a polyhedron face, have been quantified. Compared to the well established random close packing, the distributions become wider and more asymmetric with a long tail at the higher values. The volume and sphericity of each Delaunay cell have also been quantified. Their distributions are shown to be wider and more asymmetric than those for the random close packing, but the peaks are almost the same. For the wet particle packing, the correlations between Voronoi polyhedron size and shape and between Delaunay cell size and shape are more scattered. The topological and metric results are also shown to be consistent with those obtained for the packing of fine particles, although the dominant forces in forming a packing differ. The results should be useful to the quantitative understanding of the structure of loosely packed particles.     

Numerical analysis of compression mechanics of highly polydisperse granular mixtures with different PSD-s

The deformation of three-dimensional highly polydisperse packings of frictional spheres with continuous unimodal and discrete uniform particle size distributions (PSDs) under uniaxial compression was investigated, using the discrete element method. The stress transmission and elasticity parameters, i.e., the effective elastic modulus and the Poisson’s ratio of the granular assemblies were examined; these parameters are important in many engineering disciplines. The influence of the shape of the PSD on the porosity and the transmission of pressures in samples was observed; however, the shape of the PSD did not affect the stiffness and the Poisson’s ratio of polydisperse granular packings. The results revealed that, in some cases, knowledge of the grain size distribution is not a critical issue for modeling granular packings composed of non-uniformly sized spheres.     

无定形态及晶态颗粒堆积结构的三维构建及表征

采用离散元法对等径球在振动条件下堆积形成的无定形结构及晶态结构进行三维构建,并对两种堆积结构的宏观性能如堆积密度及微观性能如配位数、径向分布函数及Voronoi-Delaunay孔尺寸分布进行表征及对比。结果表明:所获得的无定形结构和晶态结构的最大相对堆积密度分别为0.64和0.74,对应的配位数分布的峰值分别为7和12,径向分布函数曲线上,晶态堆积中粒子之间的位置具有长程相关性,同时晶态结构所对应的尺寸分布较无定形结构高且窄,且整体左移。     

A geometric algorithm based on tetrahedral meshes to generate a dense polydisperse sphere packing

In the discrete element method, the packing generation of polydisperse spheres with a high packing density value is a major concern. Among the methods already developed, few algorithms can generate sphere packing with a high density value. The aim of this paper is to present a new geometric algorithm based on tetrahedral meshes to generate dense isotropic arrangements of non-overlapping spheres. The method consists of first filling in every tetrahedron with spheres in contact (i.e., hard-sphere clusters). Then, the algorithm increases the packing density value by detecting the large empty spaces and filling them with new spheres. This new geometric algorithm can also generate a complex shape structure.     

Effect of particle size ratio and contribution of particle size fractions on micromechanics of uniaxially compressed binary sphere mixtures

This paper is an extension of the recent work of Wi?cek (Granul Matter 18:42, 2016), wherein geometrical parameters of binary granular mixtures with various particle size ratio and contribution of the particle size fractions were investigated. In this study, a micromechanics of binary mixtures with various ratio of the diameter of small and large spheres and contribution of small particles was analyzed using discrete element simulations of confined uniaxial compression. The study addressed contact normal orientation distributions, global and partial contact force distributions and pressure distribution in packings of frictional spheres. Additionally, the effect of particle size ratio and contribution of particle size fractions on energy dissipation in granular mixtures was investigated. The particle size ratio in binary packings was chosen to prevent small particles from percolating through bedding. The bimodality of mixtures was found to have a strong effect on distribution of contact normal orientation and distribution of normal contact forces in binary mixtures. Stress transfer in binary packing was also determined by both, particle size ratio and volume fraction of small particles. Dissipation of energy was higher in mixtures with higher particle size ratios and decreased with increasing contribution of small spheres in system.     

DEM simulation of binary sphere packing densification under vertical vibration

The densification of random binary sphere packings subjected to vertical vibration was modeled by using the discrete element method (DEM). The influences of operating parameters such as the vibration conditions, sphere size ratio (diameter ratio of larger versus small spheres), and composition (volume fraction of large spheres) of the binary mixture on the fractional packing density φ (defined as the volume of spheres divided by the volume of container) were studied. Two packing states, i.e., random loose packing (RLP) and random close packing (RCP), were reproduced and their micro properties such as the coordination number (CN), radial distribution function (RDF), and force structure were characterized and compared. The results indicate that properly controlling vibration conditions can realize the transition of binary packing structure from the RLP to RCP state when the sphere size ratio and composition are fixed, and the fractional packing density for RCP after vibration can reach φ_RCP?≈?0.86. Different packing characteristics from RLP and RCP identify that RCP shows much denser and more uniform structure than RLP. The current modeling results are in good agreement with those obtained from both the physical experiments and the proposed empirical models in the literature.     

Granular gases in mechanical engineering: on the origin of heterogeneous ultrasonic shot peening

The behavior of an ultrasonic shot peening process is observed and analyzed by using a model of inelastic hard spheres in a gravitational field that are fluidized by a vibrating bottom wall (sonotrode) in a cylindrical chamber. A marked heterogeneous distribution of impacts appears when the collision between the shot and the side wall becomes inelastic with constant dissipation. This effect is one order of magnitude larger than the simple heterogeneity arising from boundary collision on the cylinder. Variable restitution coefficients bring the simulation closer to the general observation and allow the investigation of peening regimes with changing shot density. We compute within this model other physical quantities (impact velocities, impact angle, temperature and density profile) that are influenced by the number N of spheres.