Self-assembly of granular particles is of great interest in both applied and basic research. It is commonly observed that when randomly packed into a container, granular particles form disordered structures like glass. As the particles are athermal, the self-assembly of such packings can normally be directed with energy input via vibration or shear. However, here we show that in particular containers, mono-sized spheres and cubes can self-assemble into perfect crystals when randomly dropped in. This is because the favourable microstates for new particles are jammed in the ordered structure by the existing particles and the boundary synergistically. Such a self-assembly method has not been reported in the literature. It indicates that disordered packing structure may result from the conflict between the internal structure and the structure shaped by the boundary. Therefore, to bridge such inconsistency could be a general principle for directing self-assembly for different kinds of particles in emerging areas.
Static granular packings are model hard-sphere glass formers. The nature of glass transition has remained a hotly debated issue. We review recent experimental progresses in using granular materials to study glass transitions. We focus on the growth of glass order with five-fold symmetry in granular packings and relate the findings to both geometric frustration and random first-order phase transition theories.
We study the internal dynamical processes taking place in a granular packing below yield stress. At all packing fractions and down to vanishingly low applied shear, a logarithmic creep is evidenced. The experiments are analyzed under the scope of a visco-elastic model introducing an internal "fluidity" variable. For all experiments, the creep dynamics can be rescaled onto a unique curve which displays jamming at the random-close-packing limit. At each packing fraction, a stress value is evidenced, corresponding to the onset of internal granular reorganisation leading to a slowing down the cree…
Dependence of structural self-organization of granular materials on preparation and grain parameters is key to predictive modelling. We study 60 different mechanically equilibrated polydisperse disc packs, generated numerically by two protocols. We show that, for same-variance disc size distributions (DSDs): 1. the mean coordination number of rattler-free packs vs. the packing fraction is a function independent of initial conditions, friction and the DSD: 2. all quadron volume and cell order distributions collapse to universal forms, also independent of the above. We conclude that, contrary to…
We have performed a novel experiment on granular packs composed of automatically swelling particles. By analyzing the Voronoi structure of packs going through the jamming transition, we show that the local configuration of a jamming pack is strikingly similar to that of a glass-forming liquid, both in terms of their universal area distribution and the process of defect annealing. Furthermore, we demonstrate that an unambiguous structural signature of the jamming transition can be obtained from the pair correlation functions of a pack. Our study provides insights into the structural properties …
We study the structural properties of two-dimensional granular packings prepared by random deposition from a source line. We consider a class of random ballistic deposition models based on single-particle relaxation rules controlled by a critical angle, and we show that these local rules can be formulated as rolling friction in the framework of dynamic methods for the simulation of granular materials. We find that a packing prepared by random deposition models is generically unstable, and undergoes dynamic rearrangements. As a result, the dynamic method leads systematically to a higher solid f…
Scattering methods are widespread used to characterize the structure and constituents of matter on small length scales. This motivates this introductory text on identifying prospective approaches to scattering-based methods for granular media. A survey to light scattering by particles and particle ensembles is given. It is elaborated why the established scattering methods using X-rays and visible light cannot in general be transferred to granular media. Spectroscopic measurements using Terahertz radiation are highlighted as they to probe the scattering properties of granular media, which are s…
Structural characteristics are considered to be the dominant factors in determining the effective properties of granular media, particularly in the scope of transport phenomena. Towards improved heat management, thermal transport in granular media requires an improved fundamental understanding. In this study, the effects of packing structure on heat transfer in granular media are evaluated at macro- and grain-scales. At the grain-scale, a gas-solid coupling heat transfer model is adapted into a discrete-element-method to simulate this transport phenomenon. The numerical framework is validated …
The notion of random close packings of a bulk static collection of ball bearings or sand grains was introduced in the 1960's by G.D. Scott and J.D. Bernal. There have been numerous attempts to understand the packings. We give a short argument, based on recent experiments and simulations, which explains the packings in purely geometric terms.
In this letter, we present the first experimental study of bridge structures in three-dimensional dry granular packings. When bridges are small, they are predominantly 'linear', and have an exponential size distribution. Larger, predominantly 'complex' bridges, are confirmed to follow a power-law size distribution. Our experiments, which use X-ray tomography, are in good agreement with the simulations presented here, for the distribution of sizes, end-to-end lengths, base extensions and orientations of predominantly linear bridges. Quantitative differences between the present experiment and ea…
We experimentally study the transition from steady flow to unsteady flow in a quasi-2D granular heap when small amounts of water are added to monodisperse glass spheres. Particles flow uniformly down both sides of the heap for low water content, but unsteady flow occurs as the water content increases. The unsteady flow mode consists of a non-depositing downslope avalanche and an upslope propagating granular jump. The transition from steady to unsteady flow occurs when the slope exceeds a critical angle as a result of water-induced cohesion. Under unsteady flow conditions, the deposited heap co…
It has been recently pointed out that local volume fluctuations in granular packings follow remarkably well a shifted and rescaled Gamma distribution named the kGamma distribution [T. Aste, T. Di Matteo, Phys. Rev. E 77 (2008) 021309]. In this paper we confirm, extend and discuss this finding by supporting it with additional experimental and simulation data.
We study the packing fraction of clusters in free-falling streams of spherical and irregularly shaped particles using flash X-ray radiography. The estimated packing fraction of clusters is low enough to correspond to coordination numbers less than 6. Such coordination numbers in numerical simulations correspond to aggregates that collide and grow without bouncing. Moreover, the streams of irregular particles evolved faster and formed clusters of larger sizes with lower packing fraction. This result on granular streams suggests that particle shape has a significant effect on the agglomeration p…
We investigate how forces spread through frictionless granular packs at the jamming transition. Previous work has indicated that such packs are isostatic, and thus obey a null stress law which, independent of the packing history, causes rays of stress to propagate away from a point force at oblique angles. Prior verifications of the null stress law have used a sequential packing method which yields packs with anisotropic packing histories. We create packs without this anisotropy, and then later break the symmetry by adding a boundary. Our isotropic packs are very sensitive, and their responses…
We experimentally study a two-dimensional (2D) granular pack of photoelastic disks subject to vertical manual tapping. Using bright and dark field images, we employ gradient-based image analysis methods to analyse various structural quantities. These include the packing fraction ($ϕ$), force per disk ($F_d$) and force chain segment length ($l$) as a function of the tapping number ($τ$). The increase in packing fraction with tapping number is found to exponentially approach an asymptotic value. An exponential distribution is observed for both the cumulative numbers of force per disk $F_d$ : $N_…
The topological structure resulting from the network of contacts between grains (contact network) is studied for very large samples of disorderly-packed monosized spheres with densities ranging from 0.58 to 0.64. The hierarchical organization of such a structure is studied by means of a topological map which starts from a given sphere and moves outwards in concentric shells through the contact network. We find that the topological density of disordered sphere packing is larger than the topological density of equivalent lattice sphere packings.
This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to $1$, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increase…
Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction and other dissipative interactions. The resistance to rolling and spinning/twisting torque that stops a sphere also changes the microstructure of a granular packing of frictional spheres by increasing the number of constraints on the degrees of freedom of motion. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a pressure-controlled protocol. Mechanically stable packings are achievable at volume fractions and…
We present an experimental investigation of the probability distribution of normal contact forces, $P(F)$, at the bottom boundary of static three dimensional packings of compressible granular materials. We find that the degree of deformation of individual grains plays a large role in determining the form of this distribution. For small amounts of deformation we find a small peak in $P(F)$ below the mean force with an exponential tail for forces larger than the mean force. As the degree of deformation is increased the peak at the mean force grows in height and the slope of the exponential tail …
We simulate vertically shaken dense granular packings with horizontal periodic boundary conditions. A coordinated translating motion of the whole medium emerges when the horizontal symmetry is broken by disorder or defects in the packing and the shaking is weak enough to conserve the structure. We argue that such a drift originates in the interplay between structural symmetry breaking and frictional forces transmitted by the vibrating plate. A non-linear ratchet model with stick-slips reproduces many faces of the phenomenon. The collective motion discussed here underlies phenomena observed rec…
We measure the two-point density correlations and Voronoi cell distributions of cyclically sheared granular spheres obtained with a fluorescence technique and compare them with random packing of frictionless spheres. We find that the radial distribution function $g(r)$ is captured by the Percus-Yevick equation for initial volume fraction $ϕ=0.59$. However, small but systematic deviations are observed because of the splitting of the second peak as $ϕ$ is increased towards random close packing. The distribution of the Voronoi free volumes deviates from postulated $Γ$ distributions, and the orien…
We identify arches in a bed of granular disks generated by a molecular dynamic-type simulation. We use the history of the deposition of the particles to identify the supporting contacts of each particle. Then, arches are defined as sets of mutually stable disks. Different packings generated through tapping are analyzed. The possibility of identifying arches from the static structure of a deposited bed, without any information on the history of the deposition, is discussed.
The developing structure in systems of compacting ductile grains were studied experimentally in two and three dimensions. In both dimensions, the peaks of the radial distribution function were reduced, broadened, and shifted compared with those observed in hard disk- and sphere systems. The geometrical three--grain configurations contributing to the second peak in the radial distribution function showed few but interesting differences between the initial and final stages of the two dimensional compaction. The evolution of the average coordination number as function of packing fraction is compa…
The transmission rules of interparticle forces between granular particles were analyzed, and a discrete packing model was proposed to calculate the static pressure at the bottom of granular material confined in a vertical column. The mechanical analysis and numerical simulation results indicate that the silo effect is caused by the frictional contacts between border particles and inner walls, the static pressure at the bottom depends on the external load initially, and then tends to a saturation pressure (Pn) in an exponential form. The saturation pressure (Pn) is positive linear related to th…
Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among more than two spheres, shows that the structural organization can be conveniently studied in terms of a space-filling packing of irregular tetrahedra. The study of the volume distribution of such tetrahedra reveals an exponential decay in the region of large volumes; a behavior that is in very good quantitative agreement with theoretical prediction. I argue …
Starting from three-dimensional volume data of a granular packing, as e.g. obtained by X-ray Computed Tomography, we discuss methods to first detect the individual particles in the sample and then analyze their properties. This analysis includes the pair correlation function, the volume and shape of the Voronoi cells and the number and type of contacts formed between individual particles. We mainly focus on packings of monodisperse spheres, but we will also comment on other monoschematic particles such as ellipsoids and tetrahedra. This paper is accompanied by a package of free software contai…
We present a systematic investigation of the distribution of normal forces at the boundaries of static packings of spheres. A new method for the efficient construction of large hexagonal-close-packed crystals is introduced and used to study the effect of spatial ordering on the distribution of forces. Under uniaxial compression we find that the form for the probability distribution of normal forces between particles does not depend strongly on crystallinity or inter-particle friction. In all cases the distribution decays exponentially at large forces and shows a plateau or possibly a small pea…
We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate $N=\mathcal{O}(10^6)$ particles or more. As a first application we consider a dense granular packing which is fluidized by an upward stream of liquid, i.e. a fluidized bed. In the stationary state, when all forces balance, we always observe a well defined interface whose width is approximately independent of packing fraction. We also study the dynamics of expansion and sedimentation after a sudden change in flow rate giving rise to a change in sta…
We examine the impact of a solid sphere into a fine-grained granular bed. Using high-speed X-ray radiography we track both the motion of the sphere and local changes in the bed packing fraction. Varying the initial packing density as well as the ambient gas pressure, we find a complete reversal in the effect of interstitial gas on the impact response of the bed: The dynamic coupling between gas and grains allows for easier penetration in initially loose beds but impedes penetration in more densely packed beds. High-speed imaging of the local packing density shows that these seemingly incongruo…
We present numerical evidence for an additional discontinuous transition inside the jammed regime for an asymmetric bidisperse granular packing upon compression. This additional transition line separates jammed states with networks of predominantly large particles from jammed networks formed by both large and small particles, and the transition is indicated by a discontinuity in the number of particles contributing to the jammed network. The additional transition line emerges from the curves of jamming transitions and terminates in an end-point where the discontinuity vanishes. The additional …
Many clays, soils, biological tissues, foods, and coatings are shrinkable, granular materials: they are composed of packed, hydrated grains that shrink when dried. In many cases, these packings crack during drying, critically hindering applications. However, while cracking has been widely studied for bulk gels and packings of non-shrinkable grains, little is known about how packings of shrinkable grains crack. Here, we elucidate how grain shrinkage alters cracking during drying. Using experiments with model shrinkable hydrogel beads, we show that differential shrinkage can dramatically alter c…
Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a longstanding question in the field of granular matter. Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation …
The structure and stresses of static granular packs in cylindrical containers are studied using large-scale discrete element molecular dynamics simulations in three dimensions. We generate packings by both pouring and sedimentation and examine how the final state depends on the method of construction. The vertical stress becomes depth-independent for deep piles and we compare these stress depth-profiles to the classical Janssen theory. The majority of the tangential forces for particle-wall contacts are found to be close to the Coulomb failure criterion, in agreement with the theory of Janssen…
Rigid particles pack into structures, such as sand dunes on the beach, whose overall stability is determined by the average number of contacts between particles. However, when packing spatially extended objects with flexible shapes, additional concepts must be invoked to understand the stability of the resulting structure. Here we study the disordered packing of chains constructed out of flexibly-connected hard spheres. Using X-ray tomography, we find long chains pack into a low-density structure whose mechanical rigidity is mainly provided by the backbone. On compaction, randomly-oriented, se…
Granular crystallisation is an important phenomenon whereby ordered packing structures form in granular matter under vibration. However, compared with the well-developed principles of crystallisation at the atomic scale, crystallisation in granular matter remains relatively poorly understood. To investigate this behaviour further and bridge the fields of granular matter and materials science, we simulated mono-disperse spheres confined in cylindrical containers to study their structural dynamics during vibration. By applying adequate vibration, disorder-to-order transitions were induced. Such …
Granular material exposed to shear shows a variety of unique phenomena: Reynolds dilatancy, positional order and orientational order effects may compete in the shear zone. We study granular packings consisting of macroscopic prolate, oblate and spherical grains and compare their behaviour. X-ray tomography is used to determine the particle positions and orientations in a cylindrical split bottom shear cell. Packing densities and the arrangements of individual particles in the shear zone are evaluated. For anisometric particles, we observe the competition of two opposite effects. One the one ha…
We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed Spot Model, where particles in a dense random packing undergo chain-like collective displacements in response to diffusing "spots" of influence, carrying a slight excess of interstitial free volume. We reconstruct the microscopic dynamics of particles from the "coarse grained" dynamics of spots by introducing a localized particle relaxation step after each spot-induced block displacement, simply to enf…
The simulation of granular media is usually done either with event-driven codes that treat collisions as instantaneous but have difficulty with very dense packings, or with molecular dynamics methods that approximate rigid grains using a stiff viscoelastic spring. There is a little-known method that combines several collision events into a single timestep in order to retain the instantaneous collisions of event-driven dynamics but also be able to handle dense packings. However, it is poorly characterized as to its regime of validity and failure modes. We present a modification of this method t…
We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic, cylindrical granular material, using high-resolution capacitive monitoring. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical vibrations evolve to a dense, highly ordered, nematic state in which the long particle axes align with the vertical tube walls. We find that the orientational ordering process is reflected in a characteristic, steep rise in the local packing fraction. At any given height inside th…
We present numerical simulations that allow us to compute the number of ways in which $N$ particles can pack into a given volume $V$. Our technique modifies the method of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011)) and outperforms existing direct enumeration methods by more than 200 orders of magnitude. We use our approach to study the system size dependence of the number of distinct packings of a system of up to 128 poly-disperse soft disks. We show that, even though granular particles are distinguishable, we have to include a factor $1/N!$ to ensure that the entropy does not change when …
Tap density of a granular powder is often linked to the flowability via Carr Index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in literature: The inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept, we obtain the tap density equa…
If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a solution to this inverse-packing problem by framing it in the context of artificial evolution. By representing shapes as bonded spheres, we show how shapes may be mutated, simulated, and selected to produce particularly dense or loose packing aggregates, both with and without friction. Moreover, we show how motifs emerge linking these shapes together. The resu…
What particle shape will generate the highest packing fraction when randomly poured into a container? In order to explore and navigate the enormous search space efficiently, we pair molecular dynamics simulations with artificial evolution. Arbitrary particle shape is represented by a set of overlapping spheres of varying diameter, enabling us to approximate smooth surfaces with a resolution proportional to the number of spheres included. We discover a family of planar triangular particles, whose packing fraction of $ϕ\sim$ 0.73 outpaces almost all reported experimental results for random packi…
The effects of movement of the side walls of a confined granular packing are studied by discrete element, molecular dynamics simulations. The dynamical evolution of the stress is studied as a function of wall movement both in the direction of gravity as well as opposite to it. For all wall velocities explored, the stress in the final state of the system after wall movement is fundamentally different from the original state obtained by pouring particles into the container and letting them settle under the influence of gravity. The original packing possesses a hydrostatic-like region at the top …
Under external perturbations, inter-particle forces in disordered granular media are well known to form a heterogeneous distribution with filamentary patterns. Better understanding these forces and the distribution is important for predicting the collective behavior of granular media, the media second only to water as the most manipulated material in global industry. However, studies in this regard so far have been largely confined to granular media exhibiting only geometric heterogeneity, leaving the dimension of mechanical heterogeneity a rather uncharted area. Here, through a FEM contact me…
We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly non-affine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number.
We investigate the two-dimensional packing of extremely prolate (aspect ratio $α=L/D>10$) granular materials, comparing experiments with Monte-Carlo simulations. The average packing fraction of particles with aspect ratio $α=12$ is $0.68\pm0.03$. We quantify the orientational correlation of particles and find a correlation length of two particle lengths. The functional form of the decay of orientational correlation is the same in both experiments and simulations spanning three orders of magnitude in aspect ratio. This function decays over a distance of two particle lengths. It is possible to i…
We show how rigidity emerges in experiments of sheared frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity percolation, agree with each other and identify similar rigid structures. As the system becomes jammed, at a contact number of $z=2.4\pm 0.1$, a rigid backbone interspersed with floppy, particle-filled holes of a broad range of sizes emerges, creating a sponge-like morphology. We also find that the pressure within rigid structures always exceeds the pressur…
If you walk on sand, it supports your weight. How do the disordered forces between particles in sand organize, to keep you from sinking? This simple question is surprisingly difficult to answer experimentally: measuring forces in three dimensions, between deeply buried grains, is challenging. We describe here experiments in which we have succeeded in measuring forces inside a granular packing subject to controlled deformations. We connect the measured micro-scale forces to the macro-scale packing force response with an averaging, mean field calculation. This calculation explains how the combin…
Simulated granular packings with different particle friction coefficient mu are examined. The distribution of the particle-particle and particle-wall normal and tangential contact forces P(f) are computed and compared with existing experimental data. Here f equivalent to F/F-bar is the contact force F normalized by the average value F-bar. P(f) exhibits exponential-like decay at large forces, a plateau/peak near f = 1, with additional features at forces smaller than the average that depend on mu. Computations of the force-force spatial distribution function and the contact point radial distrib…
We present measurements of the stress response of packings formed from a wide range of particle shapes. Besides spheres these include convex shapes such as the Platonic solids, truncated tetrahedra, and triangular bipyramids, as well as more complex, non-convex geometries such as hexapods with various arm lengths, dolos, and tetrahedral frames. All particles were 3D-printed in hard resin. Well-defined initial packing states were established through preconditioning by cyclic loading under given confinement pressure. Starting from such initial states, stress-strain relationships for axial compre…
We study wave propagation in two-dimensional granular crystals under the Hertzian contact law consisting of hexagonal packings of spheres under various basin geometries including hexagonal, triangular, and circular basins which can be tiled with hexagons. We find that the basin geometry will influence wave reflection at the boundaries, as expected, and also may result in bottlenecks forming. While exterior strikers the size of a single sphere have been considered in the literature, it is also possible to consider strikers which impact multiple spheres along a boundary, or to have multiple side…
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a "hidden" polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Ad…
We apply two theoretical and two numerical methods to the problem of a disk placed in a groove and subjected to gravity and a torque. Methods assuming rigid particles are indeterminate -- certain combinations of forces cannot be calculated, but only constrained by inequalities. In methods assuming deformable particles, these combinations of forces are determined by the history of the packing. Thus indeterminacy in rigid particles becomes memory in deformable ones. Furthermore, the torque needed to rotate the particle was calculated. Two different paths to motion were identified. In the first, …
