Stress distribution of faceted particles in a silo after its partial discharge

Nonlinear effect of grain elongation on the flow rate in silo discharge

By means of two-dimensional numerical simulations based on contact dynamics, we present a systematic analysis of the joint effects of grain shape (i.e., grain elongation) and system size on silo discharge for increasing orifice sizes D. Grains are rounded-cap rectangles whose aspect ratio are varied from 1 (disks) to 7. In order to clearly isolate the effect of grain shape, the mass of the grains is keeping constant as well as the condition of the discharge by reintroducing the exiting grains at the top of the silo. In order to quantify the possible size effects, the thickness W of the silos is varied from 7 to 70 grains diameter, while keeping the silos aspect ratio always equal to 2. We find that, as long as size effects are negligible, the flow rate Q increases as a Beverloo-like function with D, also for the most elongated grains. In contrast, the effects of grain elongation on the flow rate depend on orifice size. For small normalized orifice sizes, the flow rate is nearly independent with grain elongation. For intermediate normalized orifice sizes the flow rate first increases with grain elongation up to a maximum value that depends on the normalized size of the orifice and saturates as the grains become more elongated. For larger normalized orifice size, the flow rate is an increasing function of grains' aspect ratio. Velocity profiles and packing fraction profiles close to the orifice turn out to be self-similar for all grain shapes and for the whole range of orifice and system sizes studied. Following the methodology introduced by Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.248001], we explain the nonlinear variation of Q with grain elongation, and for all orifice sizes, from compensation mechanisms between the velocity and packing fraction measured at the center of the orifice. Finally, an equation to predict the evolution of Q as a function of the aspect ratio of the grains is deduced.

Effects of particle shape mixture on strength and structure of sheared granular materials

Using bi-dimensional discrete element simulations, the shear strength and microstructure of granular mixtures composed of particles of different shapes are systematically analyzed as a function of the proportion of grains of a given number of sides and the combination of different shapes (species) in one sample. We varied the angularity of the particles by varying the number of sides of the polygons from 3 (triangles) up to 20 (icosagons) and disks. The samples analyzed were built keeping in mind the following cases: (1) increase of angularity and species starting from disks; (2) decrease of angularity and increase of species starting from triangles; (3) random angularity and increase of species starting from disks and from polygons. The results show that the shear strength vary monotonically with increasing numbers of species (it may increase or decrease), even in the random mixtures (case 3). At the micro-scale, the variation in shear strength as a function of the number of species is due to different mechanisms depending on the cases analyzed. It may result from the increase of both the geometrical and force anisotropies, from only a decrease of frictional anisotropy, or from compensation mechanisms involving geometrical and force anisotropies.

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.

Active particles with desired orientation flowing through a bottleneck

We report extensive numerical simulations of the flow of anisotropic self-propelled particles through a constriction. In particular, we explore the role of the particles’ desired orientation with respect to the moving direction on the system flowability. We observe that when particles propel along the direction of their long axis (longitudinal orientation) the flow-rate notably reduces compared with the case of propulsion along the short axis (transversal orientation). And this is so even when the effective section (measured as the number of particles that are necessary to span the whole outlet) is larger for the case of longitudinal propulsion. This counterintuitive result is explained in terms of the formation of clogging structures at the outlet, which are revealed to have higher stability when the particles align along the long axis. This generic result might be applied to many different systems flowing through bottlenecks such as microbial populations or different kind of cells. Indeed, it has already a straightforward connection with recent results of pedestrian (which self-propel transversally oriented) and mice or sheep (which self-propel longitudinally oriented).

Experimental Study of Ordering of Hard Cubes by Shearing

We experimentally analyze the compaction dynamics of an ensemble of cubic particles submitted to a novel type of excitation. Instead of the standard tapping procedure used in granular materials we apply alternative twists to the cylindrical container. Under this agitation, the development of shear forces among the different layers of cubes leads to particle alignment. As a result, the packing fraction grows monotonically with the number of twists. If the intensity of the excitations is sufficiently large, an ordered final state is reached where the volume fraction is the densest possible compatible with the boundary condition. This ordered final state resembles the tetratic or cubatic phases observed in colloids.

Simulating competitive egress of noncircular pedestrians

We present a numerical framework to simulate pedestrian dynamics in highly competitive conditions by means of a force-based model implemented with spherocylindrical particles instead of the traditional, symmetric disks. This modification of the individuals' shape allows one to naturally reproduce recent experimental findings of room evacuations through narrow doors in situations where the contact pressure among the pedestrians was rather large. In particular, we obtain a power-law tail distribution of the time lapses between the passage of consecutive individuals. In addition, we show that this improvement leads to new features where the particles' rotation acquires great significance.

Outflow and clogging of shape-anisotropic grains in hoppers with small apertures

Outflow of granular material through a small orifice is a fundamental process in many industrial fields, for example in silo discharge, and in everyday's life. Most experimental studies of the dynamics have been performed so far with monodisperse disks in two-dimensional (2D) hoppers or spherical grains in 3D. We investigate this process for shape-anisotropic grains in 3D hoppers and discuss the role of size and shape parameters on avalanche statistics, clogging states, and mean flow velocities. It is shown that an increasing aspect ratio of the grains leads to lower flow rates and higher clogging probabilities compared to spherical grains. On the other hand, the number of grains forming the clog is larger for elongated grains of comparable volumes, and the long axis of these blocking grains is preferentially aligned towards the center of the orifice. We find a qualitative transition in the hopper discharge behavior for aspect ratios larger than ≈6. At still higher aspect ratios >8-12, the outflowing material leaves long vertical holes in the hopper that penetrate the complete granular bed. This changes the discharge characteristics qualitatively.

Particle alignment and clustering in sheared granular materials composed of platy particles

By means of molecular dynamics simulations, we investigate the texture and local ordering in sheared packings composed of cohesionless platy particles. The morphology of large packings of platy particles in quasistatic equilibrium is complex due to the combined effects of local nematic ordering of the particles and anisotropic orientations of contacts between particles. We find that particle alignment is strongly enhanced by the degree of platyness and leads to the formation of face-connected clusters of exponentially decaying size. Interestingly, due to dynamics in continuous shearing, this ordering phenomenon emerges even in systems composed of particles of very low platyness differing only slightly from spherical shape. The number of clusters is an increasing function of platyness. However, at high platyness the proportion of face-face interactions is too low to allow for their percolation throughout the system.

Packings of irregular polyhedral particles: strength, structure, and effects of angularity

We present a systematic numerical investigation of the shear strength and structure of granular packings composed of irregular polyhedral particles. The angularity of the particles is varied by increasing the number of faces from 8 (octahedronlike shape) to 596. We find that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below 46 faces). At the same time, the packing fraction increases to a peak value but declines for more angular particles. We analyze the connectivity and anisotropy of the microstructure by considering both the contacts and branch vectors joining particle centers. The increase of the shear strength with angularity is shown to be due to a net increase of the fabric and force anisotropies but at higher particle angularity a rapid falloff of the fabric anisotropy is compensated by an increase of force anisotropy, leading thus to the saturation of shear strength.

Influence of the feeding mechanism on deposits of square particles

In a previous paper [Hidalgo et al., Phys. Rev. Lett. 103, 118001 (2009)] it was shown that square particles deposited in a silo tend to align with a diagonal parallel to the gravity, giving rise to a deposit with very particular properties. Here we explore, both experimentally and numerically, the effect on these properties of the filling mechanism. In particular, we modify the volume fraction of the initial configuration from which the grains are deposited. Starting from a very dilute case, increasing the volume fraction results in an enhancement of the disorder in the final deposit characterized by a decrease of the final packing fraction and a reduction of the number of particles oriented with their diagonal in the direction of gravity. However, for very high initial volume fractions, the final packing fraction increases again. This result implies that two deposits with the same final packing fraction can be obtained from very different initial conditions. The structural properties of such deposits are analyzed, revealing that, although the final volume fraction is the same, their micromechanical properties notably differ.

Nonlinear effects of particle shape angularity in sheared granular media

We analyze the effects of particle shape angularity on the macroscopic shear behavior and texture of granular packings simulated by means of the contact dynamics method. The particles are regular polygons with an increasing number of sides ranging from 3 (triangles) to 60. The packings are analyzed in the steady shear state in terms of their shear strength, packing fraction, connectivity, and fabric and force anisotropies, as functions of the angularity. An interesting finding is that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below six sides). In contrast, the packing fraction declines towards a constant value, so that the packings of more angular particles are looser but have higher shear strength. We show that the increase of the shear strength at low angularity is due to an increase of both contact and force anisotropies and the saturation of the shear strength for higher angularities is a consequence of a rapid falloff of the contact and normal force anisotropies compensated for by an increase of the tangential force anisotropy. This transition reflects clearly the rather special geometrical properties of these highly angular shapes, implying that the stability of the packing relies strongly on the side-side contacts and the mobilization of friction forces.

Discrete simulation of dense flows of polyhedral grains down a rough inclined plane

The influence of grain angularity on the properties of dense flows down a rough inclined plane are investigated. Three-dimensional numerical simulations using the nonsmooth contact dynamics method are carried out with both spherical (rounded) and polyhedral (angular) grain assemblies. Both sphere and polyhedra assemblies abide by the flow start and stop laws, although much higher tilt angle values are required to trigger polyhedral grain flow. In the dense permanent flow regime, both systems show similarities in the bulk of the material (away from the top free surface and the substrate), such as uniform values of the solid fraction, inertial number and coordination number, or linear dependency of the solid fraction and effective friction coefficient with the inertial number. However, discrepancies are also observed between spherical and polyhedral particle flows. A dead (or nearly arrested) zone appears in polyhedral grain flows close to the rough bottom surface, reflected by locally concave velocity profiles, locally larger coordination number and solid fraction values, smaller inertial number values. This dead zone disappears for smooth bottom surfaces. In addition, unlike sphere assemblies, polyhedral grain assemblies exhibit significant normal stress differences, which increase close to the substrate.

Force chains and contact network topology in sheared packings of elongated particles

By means of contact dynamic simulations, we investigate the contact network topology and force chains in two-dimensional packings of elongated particles subjected to biaxial shearing. The morphology of large packings of elongated particles in quasistatic equilibrium is complex due to the combined effects of local nematic ordering of the particles and orientations of contacts between particles. The effect of elongation on shear behavior and dilatancy was investigated in detail in a previous paper [Azéma and Radjai, Phys. Rev. E 81, 051304 (2010)]. Here, we show how particle elongation affects force distributions and force-fabric anisotropy via various local structures allowed by steric exclusions and the requirement of force balance. We find that the force distributions become increasingly broader as particles become more elongated. Interestingly, the weak force network transforms from a passive stabilizing agent with respect to strong force chains to an active force-transmitting network for the whole system. The strongest force chains are carried by side-side contacts oriented along the principal stress direction.