Dynamic rearrangements and packing regimes in randomly deposited two-dimensional granular beds

Microstructural analysis of sheared polydisperse polyhedral grains

This article presents an analysis of the shear strength of numerical samples composed of polyhedra presenting a grain size dispersion. Previous numerical studies using, for instance, disks, polygons, and spheres, have consistently shown that microstructural properties linked to the fabric and force transmission allow granular media to exhibit a constant shear resistance although packing fraction can dramatically change as a broader grain-size distribution is considered. To have a complete picture of such behavior, we developed a set of numerical experiments in the frame of the discrete element method to test the shear strength of polydisperse samples composed of polyhedral grains. Although the contact networks and force transmission are quite more complex for such generalized grain shape, we can verify that the shear strength independence still holds up for 3D regular polyhedra. We make a particular focus upon the role of different contact types in the assemblies and their relative contributions to the granular connectivity and sample strength. The invariance of shear strength at the macroscopic scale results deeply linked to fine compensations at the microstructural level involving geometrical and force anisotropies of the assembly.

Rheology of granular materials composed of crushable particles

We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.

Bonded-cell model for particle fracture

Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.

Cohesive granular materials composed of nonconvex particles

The macroscopic cohesion of granular materials made up of sticky particles depends on the particle shapes. We address this issue by performing contact dynamics simulations of 2D packings of nonconvex aggregates. We find that the macroscopic cohesion is strongly dependent on the strain and stress inhomogeneities developing inside the material. The largest cohesion is obtained for nearly homogeneous deformation at the beginning of unconfined axial compression and it evolves linearly with nonconvexity. Interestingly, the aggregates in a sheared packing tend to form more contacts with fewer neighboring aggregates as the degree of nonconvexity increases. We also find that shearing leads either to an isotropic distribution of tensile contacts or to the same privileged direction as that of compressive contacts.

Towards a description of particulate fouling: from single particle deposition to clogging

Particulate fouling generally arises from the continuous deposition of colloidal particles on initially clean surfaces, a process which can even lead to a complete blockage of the fluid cross-section. In the present paper, the initial stages of the fouling process (which include single-particle deposition and reentrainment) are first addressed and current modelling state-of-the-art for particle-turbulence and particle-wall interactions is presented. Then, attention is specifically focused on the later stages (which include multilayer formation, clogging and blockage). A detailed review of experimental works brings out the essential mechanisms occurring during these later stages: as for the initial stages, it is found that clogging results from the competition between particle-fluid, particle-surface and particle-particle interactions. Numerical models that have been proposed to reproduce the later stages of fouling are then assessed and a new Lagrangian stochastic approach to clogging in industrial cases is detailed. These models further confirm that, depending on hydrodynamical conditions (the flow velocity), fluid characteristics (such as the ionic strength) as well as particle and substrate properties (such as zeta potentials), particle deposition can lead to the formation of either a single monolayer or multilayers. The present paper outlines also future numerical developments and experimental works that are needed to complete our understanding of the later stages of the fouling process.

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.

Rheology of granular materials composed of nonconvex particles

By means of contact dynamics simulations, we investigate the shear strength and internal structure of granular materials composed of two-dimensional nonconvex aggregates. We find that the packing fraction first grows as the nonconvexity is increased but declines at higher nonconvexity. This unmonotonic dependence reflects the competing effects of pore size reduction between convex borders of aggregates and gain in porosity at the nonconvex borders that are captured in a simple model fitting nicely the simulation data both in the isotropic and sheared packings. On the other hand, the internal angle of friction increases linearly with nonconvexity and saturates to a value independent of nonconvexity. We show that fabric anisotropy, force anisotropy, and friction mobilization, all enhanced by multiple contacts between aggregates, govern the observed increase of shear strength and its saturation with increasing nonconvexity. The main effect of interlocking is to dislocate frictional dissipation from the locked double and triple contacts between aggregates to the simple contacts between clusters of aggregates. This self-organization of particle motions allows the packing to keep a constant shear strength at high nonconvexity.

Stress-strain behavior and geometrical properties of packings of elongated particles

We present a numerical analysis of the effect of particle elongation on the quasistatic behavior of sheared granular media by means of the contact dynamics method. The particle shapes are rounded-cap rectangles characterized by their elongation. The macroscopic and microstructural properties of several packings subjected to biaxial compression are analyzed as a function of particle elongation. We find that the shear strength is an increasing linear function of elongation. Performing an additive decomposition of the stress tensor based on a harmonic approximation of the angular dependence of branch vectors, contact normals, and forces, we show that the increasing mobilization of friction force and the associated anisotropy are key effects of particle elongation. These effects are correlated with partial nematic ordering of the particles which tend to be oriented perpendicular to the major principal stress direction and form side-to-side contacts. However, the force transmission is found to be mainly guided by cap-to-side contacts, which represent the largest fraction of contacts for the most elongated particles. Another interesting finding is that, in contrast to shear strength, the solid fraction first increases with particle elongation but declines as the particles become more elongated. It is also remarkable that the coordination number does not follow this trend so that the packings of more elongated particles are looser but more strongly connected.

Shear strength and force transmission in granular media with rolling resistance

We investigate a class of granular materials characterized by the possibility of interlocking between the particles. The interlocking is modeled by its effect through rolling resistance depending on relative rotation and normal force at the contact points and involving a single parameter analogous to the sliding friction coefficient. The model, which is introduced in the framework of the contact dynamics method, is applied to simulate the simple shear of a large granular sample. We present a detailed analysis regarding the influence of rolling and sliding friction parameters on the macroscopic response in terms of shear strength, fabric properties, and force transmission. Interestingly, two distinct regimes can be distinguished in which the steady-state shear strength is controlled by either rolling resistance or sliding friction. The relative contributions of rolling and sliding contacts to the shear strength are consistent with the same two regimes. Interlocking strongly affects the force network by enhancing the arching effect and thus increasing the relative importance of weak contact forces and torques, which is reflected in a decreasing power-law probability distribution of the contact forces and torques below the mean. Due to the combined effect of friction and interlocking, the force-carrying backbone takes an increasingly columnar aspect involving a low fraction of particles. Our data suggest that the nature of the weak contact network is strongly affected by the formation of these columns of particles which do not need to be propped laterally. In particular, in the limit of high rolling resistance and sliding friction, the role of the weak network of contacts is no longer to prop the force chains, but, like the strong contact network, to actively sustain the deviatoric load imposed on the system.

Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks

This is the first paper of a series of three, in which we report on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. The influence of various assembling processes on packing microstructures is investigated. It is accurately checked that frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, higher solid fractions corresponding to more ordered configurations with traces of crystallization. Specific properties directly related to isostaticity of the force-carrying structure in the rigid limit are discussed. With frictional grains, different preparation procedures result in quite different inner structures that cannot be classified by the sole density. If partly or completely lubricated they will assemble like frictionless ones, approaching the RCP solid fraction Phi_{RCP} approximately 0.639 with a high coordination number: z* approximately =6 on the force-carrying backbone. If compressed with a realistic coefficient of friction mu=0.3 packings stabilize in a loose state with Phi approximately 0.593 and z* approximately =4.5 . And, more surprisingly, an idealized "vibration" procedure, which maintains an agitated, collisional regime up to high densities results in equally small values of z* while Phi is close to the maximum value Phi_{RCP}. Low coordination packings have a large proportion (>10%) of rattlers--grains carrying no force--the effect of which should be accounted for on studying position correlations, and also contain a small proportion of localized "floppy modes" associated with divalent grains. Low-pressure states of frictional packings retain a finite level of force indeterminacy even when assembled with the slowest compression rates simulated, except in the case when the friction coefficient tends to infinity. Different microstructures are characterized in terms of near neighbor correlations on various scales, and some comparisons with available laboratory data are reported, although values of contact coordination numbers apparently remain experimentally inaccessible.

Space-filling properties of polydisperse granular media

We present a systematic investigation of the morphology and space-filling properties of polydisperse densely packed granular media in two dimensions. A numerical procedure is introduced to generate collections of circular particles with size distributions of variable shape and span constrained by explicit criteria of statistical representativity. We characterize the domain of statistically accessible distribution parameters for a bounded number of particles. This particle generation procedure is used with two different deposition protocols in order to build large close-packed samples of prescribed polydispersity. We find that the solid fraction is a strongly nonlinear function of the size span, and the highest levels of solid fraction occur for the uniform distribution by volume fractions. As the span is increased, a transition occurs from a regime of topological disorder where the packing properties are governed by particle connectivity to a regime of metric disorder where pore-filling small particles prevail. The polydispersity manifests itself in the first regime through the variability of local coordination numbers. We observe a continuous decrease of the number of particles with four contacts and the growth of two populations of particles with three and five contacts. In the second regime, radial distribution functions show that the material is homogeneous beyond only a few average particle diameters. We also show that the packing orientational order is linked with fabric anisotropy and it declines with size span.

Force transmission in a packing of pentagonal particles

We perform a detailed analysis of the contact force network in a dense confined packing of pentagonal particles simulated by means of the contact dynamics method. The effect of particle shape is evidenced by comparing the data from pentagon packing and from a packing with identical characteristics, except for the circular shape of the particles. A counterintuitive finding of this work is that, under steady shearing, the pentagon packing develops a lower structural anisotropy than the disk packing. We show that this weakness is compensated by a higher force anisotropy, leading to enhanced shear strength of the pentagon packing. We revisit "strong" and "weak" force networks in the pentagon packing, but our simulation data also provide evidence for a large class of "very weak" forces carried mainly by vertex-to-edge contacts. The strong force chains are mostly composed of edge-to-edge contacts with a marked zigzag aspect and a decreasing exponential probability distribution as in a disk packing.

Computer simulation of model cohesive powders: influence of assembling procedure and contact laws on low consolidation states

Molecular dynamics simulations are used to investigate the structure and mechanical properties of a simple two-dimensional model of a cohesive granular material. Intergranular forces involve elasticity, Coulomb friction, and a short-range attraction akin to the van der Waals force in powders. The effects of rolling resistance (RR) at intergranular contacts are also studied. The microstructure of the cohesive packing under low pressure is shown to depend sensitively on the assembling procedure which is applied to the initially isolated particles of a granular gas. While a direct compression produces a final equilibrated configuration with a similar density to that of cohesionless systems, the formation of large aggregates prior to the application of an external pressure results in much looser stable packings. A crucial state variable is the ratio P;{*}=PaF_{0} of applied pressure P , acting on grains of diameter a , to maximum tensile contact force F0 . At low P;{*} the force-carrying structure and force distribution are sensitive to the level of velocity fluctuations in the early stages of cluster aggregation. The coordination number of packings with RR approaches 2 in the limit of low initial velocities or large rolling friction. In general the force network is composed of hyperstatic clusters, typically comprising four to a few tens of grains, in which forces reach values of the order of F0 , joined by barely rigid arms, where contact forces are very small. Under growing P;{*} , it quickly rearranges into force chainlike patterns that are more familiar in dense systems. Density correlations are interpreted in terms of a fractal structure, up to a characteristic correlation length xi of the order of ten particle diameters for the studied solid fractions. The fractal dimension in systems with RR coincides, within measurement uncertainties, with the ballistic aggregation result, in spite of a possibly different connectivity, but is apparently higher without RR. Possible effects of micromechanical and assembling process parameters on mechanical strength of packings are evoked.

Simulation study of granular compaction dynamics under vertical tapping

We study, by numerical simulation, the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking. Shaking is modeled by a series of vertical expansion of the disk packing, followed by dynamical recompression of the assembly under the action of gravity. The second phase of the shake cycle is based on an efficient event-driven molecular-dynamics algorithm. We analyze the compaction dynamics for various values of friction coefficient and coefficient of normal restitution. We find that the time evolution of the density is described by rho(t)=rho{infinity}-DeltarhoE{alpha}[-(ttau){alpha}], where E{alpha} denotes the Mittag-Leffler function of order 0<alpha<1 . The parameter tau is found to decay with tapping intensity Gamma according to a power law tau proportional, variantGamma{-gamma}, where parameter gamma is almost independent on the material properties of grains. Also, an expression for the grain mobility during the compaction process has been obtained. We characterize the local organization of disks in terms of contact connectivity and distribution of the Delaunay "free" volumes. Our analysis at microscopic scale provides evidence that compaction is mainly due to a decrease of the number of the largest pores. An interpretation of the memory effects observed for a discontinuous shift in tapping intensity Gamma is provided by the analysis of the time evolution of connectivity numbers and volume distribution of pores.