Dense Granular Materials Research Articles

Topological evolution in dense granular materials: A complex networks perspective

One of the great challenges in the science of complex materials – materials capable of emergent behavior such as self-organized pattern formation – is deciphering their “inherent” structural design principles as they deform in response to external loads. We have been exploring the efficacy of techniques from complex networks to the study of dense granular materials as a means to: (i) uncover such design principles and (ii) identify suitable metrics that quantify the evolution of structure during deformation. Herein, we characterize the developing network structure and loss of connectivity in a quasistatically deforming granular medium from the perspective of complex networks. Attention is paid to the evolution of the contact and contact force networks at the local or mesoscopic level, i.e., a particle and its immediate neighbors, as well as the macroscopic level. We explore network motifs and other topological properties at these multiple length scales, in an attempt to find that which best correlates with the constitutive properties of nonaffine deformation and dissipation, spatially and with respect to strain. Key processes or rearrangement events that cause loss of connectivity within the material domain, e.g. microbanding and force chain buckling, are investigated. Network statistics of these processes, previously shown to be major sources of energy dissipation and nonaffine deformation, are then tied to corresponding trends observed in the evolving macroscopic network. It is shown that consideration of the unweighted contact network alone is insufficient to tie dissipation to loss of material connectivity.

Mixing and segregation rates in sheared granular materials

The vertical size segregation of granular materials, a process commonly associated with the Brazil-nut effect, has generally been thought to proceed faster the greater the size difference of the particles. We experimentally investigate sheared dense bidisperse granular materials as a function of the size ratio of the two species and find that the mixing rate at low confining pressure behaves as expected from percolation-based arguments. However, we also observe an anomalous effect for the resegregation rates, wherein the segregation rate is a nonmonotonic function of the particle size ratio with a maximum for intermediate particle size ratio. Combined with the fact that increasing the confining pressure significantly suppresses both mixing and segregation rates of particles of sufficiently dissimilar size, we propose that the anomalous behavior may be attributed to a species-dependent distribution of forces within the system.

Roll-waves prediction in dense granular flows

Summary This paper analyses conditions for roll-waves formation in homogeneous granular flows with the aim of predicting their occurrence in finite length channels. With reference to a wide class of constitutive equations of the flowing medium, the response of the linearized one-dimensional flow model to a pointwise instantaneous disturbance is studied and a closed form of the Green’s function, in both stable and unstable conditions, is provided. The exponential growth of the disturbance peak is used to predict the spatial evolution of roll-waves in dry flows of dense granular materials and a criterion for the minimum channel length necessary to appreciate roll-wave development is proposed. The comparison among theoretical and experimental data available in the literature appears promising.

Critical behaviors of sheared frictionless granular materials near the jamming transition

Critical behaviors of sheared dense and frictionless granular materials in the vicinity of the jamming transition are numerically investigated. From the extensive molecular dynamics simulation, we verify the validity of the scaling theory near the jamming transition proposed by Otsuki and Hayakawa [Prog. Theor. Phys. 121, 647 (2009)]]. We also clarify the critical behaviors of the shear viscosity and the pair correlation function based on both a mean field theory and the simulation.

Modelling of dense and complex granular flow in high shear mixer granulator—A CFD approach

In the aspect of granulation process control, the numerical simulations appear to be a cost-effective and flexible tool to investigate the flow structure of granular materials in mixer granulators of various configurations and operating conditions. Computational fluid dynamics (CFD) is used in this study to model the granular flow in a vertical high shear mixer granulator. The simulation is based on the continuum model of dense-gas kinetic theory [Gidaspow, D., Bezburuah, R., Ding, J., 1992. Hydrodynamics of circulating fluidized beds, kinetic theory approach. In: Fluidization, vol. VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization, Brisbane, Australia, pp. 75–82] with consideration of inter-particle friction force at dense condition [Schaeffer, D.G., 1987. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations 66 (1), 19–50]. This study aims to verify this numerical method in modelling dense and complex granular flows, where the solids motion obtained from the simulation is validated against the experimental results of positron emission particle tracking (PEPT) technique [Ng, B.H., Kwan, C.C., Ding, Y.L., Ghadiri, M., Fan, X.F., 2007. Solids motion of calcium carbonate particles in a high shear mixer granulator: a comparison between dry and wet conditions. Powder Technology 177 (1), 1–11]. In general, the Eulerian based continuum model captures the main features of solids motion in high shear mixer granulator including the bed height and dominating flow direction (the tangential velocity). However, the continuum based kinetic-frictional model is not capable of capturing the complex vertical swirl pattern. Quantitative comparison shows over-predictions in the tangential velocity and stiff drops of the tangential velocity at the wall region. These results demonstrate the deficiency in transmitting forces in the bed of granular materials which indicate the necessity to improve the constitutive relations of dense granular materials as a continuum.

Experimental evidence of the kinematic Cosserat effect in dense granular flows

To capture shear localization in the flow of dense granular materials in a continuum description, it has earlier been proposed that granular materials be treated as Cosserat, or micropolar, continua. Here, we provide experimental verification of the kinematic Cosserat effect, or the deviation of the particle spin from the material spin induced by the velocity gradient. Contrary to earlier belief, we find this effect to be sizable even outside the shear layers. Remarkably, the particles and material elements spin in opposite directions in flow through a hopper.

Micromechanical analysis of failure propagation in frictional granular materials

AbstractThe extent to which the evolution of instabilities and failure across multiple length scales can be reproduced with the aid of a bifurcation analysis is examined. We adopt an elastoplastic micropolar constitutive model, recently developed for dense cohesionless granular materials within the framework of thermomicromechanics. The internal variables and their evolution laws are conceived from a direct consideration of the dissipative mechanism of force chain buckling. The resulting constitutive law is cast entirely in terms of the particle scale properties. It thus presents a unique opportunity to test the potential of micromechanical continuum formulations to reproduce key stages in the deformation history: the development of material instabilities and failure following an initially homogeneous deformation. Progression of failure, initiating from frictional sliding and rolling at contacts, followed by the buckling of force chains, through to macroscopic strain softening and shear banding, is reproduced. Bifurcation point, marking the onset of shear banding, occurred shortly after the peak stress ratio. A wide range of material parameters was examined to show the effect of particle scale properties on the progression of failure. Model predictions on the thickness and angle of inclination of the shear band and the structural evolution inside the band, namely the latitudinal distribution of particle rotations and the angular distributions of contacts and the normal contact forces, are consistent with observations from numerical simulations and experiments. Copyright © 2009 John Wiley & Sons, Ltd.

Probing dense granular materials by space-time dependent perturbations

The manner in which signals propagate through dense granular systems in both space and time is not well understood. In order to probe this process, we carry out discrete element simulations of the system response to excitations where we control the driving frequency and wavelength independently. Fourier analysis shows that properties of the signal depend strongly on the space-time scales of the perturbation. The features of the response provide a test bed for models that predict statistical and continuum space-time properties. We illustrate this connection between microscale physics and macroscale behavior by comparing the system response to a simple elastic model with damping.

Uniaxial compression of dense granular materials: Stress distribution and permeability

A uniaxial compression apparatus designed to investigate the dynamics of proppant particle packing is described. This dynamic compression device (DCD) uses a small charge of particles, approximately 3.5–7 cm 3 depending upon the configuration of an experiment. The DCD allows simultaneous measurement of boundary stresses on the packing and permeability of the packing to fluid flow. Visualization of the packing at compressive stress levels up to σ A = 7100 psi (49 MPa) is also demonstrated. The stresses measured are the normal stress at both walls on the axis of compression, with their difference providing a measure of the shear (or friction) force from the walls, and the transverse normal stress on one orthogonal axis, σ T . Permeability may be determined by either a fixed pressure drop or fixed flow rate experiment, with results presented from the fixed pressure drop approach by imposing a small gravity head of the flowing liquid; liquid flow is gravimetrically measured. The behaviors of packings of hard particles, both uncoated and when coated with a very viscous and tacky polyamide resin, are reported. The packing materials include a ceramic material used as a proppant in hydraulic fracturing of petroleum wells, and glass beads. The proppant and glass beads have mean diameters of approximately 700 μm and 500 μm, respectively, with the proppant less spherical and more polydisperse than the glass beads. The proppant particles undergo only limited breakage up to the maximum stress imposed here. The glass beads undergo significant breakage. Protocols for the compression can be varied. The reported results use a single loading and unloading at the same speed in each segment (increasing and decreasing stress), as well as a cyclic loading of differing numbers of cycles. The rate of loading is specified and can be varied from 0.56 μm/s–1.7 mm/s, with results here focusing on the range of 1–30 μm/s. Measured stress and permeability are shown as a function of axial load and loading rate, as well as the behavior in cyclic loading. The results are shown to be highly reproducible, establishing the ability to determine the properties of a proppant pack in a small charge device with imposed deformation. The influence of the resin coating on the properties is reported. Direct visualization is one of the key features of the DCD. Local motions and overall rearrangements of particles can be monitored by digital camera. These have been presented using particle image velocimetry (PIV).

Shock waves in rapid flows of dense granular materials: Theoretical predictions and experimental results

Strong shocks in rapid dense granular flows are studied theoretically and analyzed in detail to compare with benchmark experimental data. The experimental data includes particle image velocimetry measurements of dry granular flow following its continuous release from a silo. The rapidly moving material down the chute impinges on an obstruction wall erected perpendicular at the end of a long and steep channel. Impact leads to a sudden change in the flow regime from a fast moving supercritical thin layer to a stagnant thick heap with variable thickness. This flow configuration is particularly interesting because it is analogous to some hydraulic and aerodynamic situations. We present results about the depth and the velocity evolution and their comparisons with theoretical predictions associated with frictional granular flow equations incorporating anisotropic pressure conditions. These flow equations are integrated by implementing high-resolution nonoscillatory central differencing total variation diminishing schemes. The dynamical and geometrical effects of the flow will be discussed in detail. These include geometry evolution and depositions at supercritical and subcritical flows, the impact velocity, shock speed, its position and evolution, choice of numerical limiters, and the influence of friction angles on the dynamics and depositions. An excellent agreement between theoretical predictions and experimental observations will be demonstrated. These results can be applied to estimate impact pressures exerted by avalanches on defense structures or infrastructure along the channel and in the run-out zones, and to study the complex flow dynamics around the obstacles and in depositions when the mass comes suddenly to a standstill. Importantly, these results can form a basis for calibration of numerical simulations when strong shocks occur in granular flows.

Irreversible interaction of sound waves with dense granular matter

In this talk, we will describe quantitatively the irreversible interaction between sound and the granular medium under low confining pressure (< 0.1 MPa). Both resonance measurement and pulsed wave propagation show that as the acoustic pressure goes up to a few percent of the confining pressure, the dynamic bulk modulus and shear one can be reduced to 10% and 20%, respectively. This observation of modulus softening is qualitatively in agreement with the prediction by a model based on the Mindlin hysteretic nonlinearity at the grain contact level. Beyond certain thresholds of acoustic amplitude, the irreversible sound-granular matter interaction is accompanied by continue or intermittent sample compactions. No visible grain motion is observed at this stage; however the multiply scatted shear waves [1] allow probing a significant evolution of the contact networks, which coincide with slow recovery of elastic moduli. This work may have the implication for better understanding the physical origin of dynamic triggering of the fault core [2]. [1] X. Jia, "Coda-like multiple scattering of elastic waves in dense granular media," Phys. Rev. Lett. 93, 154303 (2004) [2] P.A. Johnson & X. Jia, "Nonlinear dynamics, granular media and dynamic earthquake triggering," Nature 437, 871-874 (2005)

Sound waves in 3D periodic granular materials

The sound propagation mechanisms inside dense granular matter, even for periodical structures, are challenging the attempts to describe it because of the discrete nature of the material. Phenomena like dissipation, scattering, and dispersion are hard to predict based on the material state and/or properties and vice-versa. We propose here a simulation method using dynamic discrete elements in order to get more insight in this problem. The small perturbation created on one side of a dense, static regular packing of grains is examined during its propagation and when it arrives at the opposite side. Both longitudinal and shear perturbation are studied and an interesting wave-acceleration is observed [1]. Moreover the rotational degree of freedom permits to observe the role of rotations in the wave propagation. The control of the inter-particle forces like, contact potential, cohesion and friction make possible to observe the effect of these micro-parameters on the macro-behavior (at the wave scale). Long term goal is to predict the large-scale macroscopic material behavior from the microscopic structure and material parameters. [1] O. Mouraille, W A Mulder and S. Luding: Sound wave acceleration in granular materials, J. Stat. Mech. (2006) P07023.

Flows of Dense Granular Media

We review flows of dense cohesionless granular materials, with a special focus on the question of constitutive equations. We first discuss the existence of a dense flow regime characterized by enduring contacts. We then emphasize that dimensional analysis strongly constrains the relation between stresses and shear rates, and show that results from experiments and simulations in different configurations support a description in terms of a frictional visco-plastic constitutive law. We then discuss the successes and limitations of this empirical rheology in light of recent alternative theoretical approaches. Finally, we briefly present depth-averaged methods developed for free surface granular flows.

Jamming, plasticity and diffusion in dense granular materials

AbstractIn this paper, we present experimental results based on photoelastic techniques that allow us to obtain complete details of processes in dense granular materials. This work focuses in particular on the jamming transition and on the nature of affine and non‐affine deformations in the shear band occuring in granular Couette flow. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Rheology of a dense granular material

In order to understand the nature of friction in dense granular materials, a discrete element simulation on granular layers subjected to isobaric plain shear is performed. It is found that the friction coefficient increases as the power of the shear rate, the exponent of which does not depend on the details of the computational model. Using a nondimensional parameter that is known as the inertial number, this power law can be cast in a generalized form so that the friction coefficients at different confining pressures collapse on the same curve. We also show that the shear rate dependence of the volume fraction obeys a power law.

Fluctuations, correlations and transitions in granular materials: statistical mechanics for a non-conventional system

In this work, we first review some general properties of dense granular materials. We are particularly concerned with a statistical description of these materials, and it is in this light that we briefly describe results from four representative studies. These are: experiment 1: determining local force statistics, vector forces, force distributions and correlations for static granular systems; experiment 2: characterizing the jamming transition, for a static two-dimensional system; experiment 3: characterizing plastic failure in dense granular materials; and experiment 4: a dynamical transition where the material 'freezes' in the presence of apparent heating for a sheared and shaken system.

Power-law friction in closely packed granular materials

In order to understand the nature of friction in dense granular materials, a discrete element simulation on granular layers subjected to isobaric plain shear is performed. It is found that the friction coefficient increases as the power of the shear rate, the exponent of which does not depend on the material constants. Using a nondimensional parameter that is known as the inertial number, the power law can be cast in a generalized form so that the friction coefficients at different confining pressures collapse on the same curve. We show that the volume fraction also obeys a power law.

Critical state plasticity. Part VI: Meso-scale finite element simulation of strain localization in discrete granular materials

Development of more accurate mathematical models of discrete granular material behavior requires a fundamental understanding of deformation and strain localization phenomena. This paper utilizes a meso-scale finite element modeling approach to obtain an accurate and thorough capture of deformation and strain localization processes in discrete granular materials such as sands. We employ critical state theory and implement an elastoplastic constitutive model for granular materials, a variant of a model called “Nor-Sand”, allowing for non-associative plastic flow and formulating it in the finite deformation regime. Unlike the previous versions of critical state plasticity models presented in a series of “Cam-Clay” papers, the present model contains an additional state parameter ψ that allows for a deviation or detachment of the yield surface from the critical state line. Depending on the sign of this state parameter, the model can reproduce plastic compaction as well as plastic dilation in either loose or dense granular materials. Through numerical examples we demonstrate how a structured spatial density variation affects the predicted strain localization patterns in dense sand specimens.

Rheophysics of dense granular materials: Discrete simulation of plane shear flows

We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I , which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.

Rheology of dense granular materials: steady, uniform flow and the avalancheregime

In the first part we present experimental results concerning the flow of a densely packedgrain collection down a two-dimensional inclined channel. For the range of inclinationscorresponding to a steady, uniform regime and to nonsliding conditions at the bottom, weobtain quasi-linear profiles of velocity, that are in contradiction with the predictions of thekinetic theory. We attribute this discrepancy to the inadequacy of the binarycollision picture in the case of dense packings. We also show that the variousvelocity profiles obtained for different flow rates and slopes merge onto a singlemaster curve, according to the following law: (d being the graindiameter, θ the channelinclination angle and θc the maximal angle of repose), provided that the regime is steady and uniform. Arguingthat continuous paths of transient contacts are effective for transporting momentum andenergy through the bulk, and that the associated dissipation time is very short compared tothe time associated with shearing, we succeed in explaining this scaling behaviour and theparadoxical nonzero shear rate in the vicinity of the free surface. We also show thatfor dense particulate flows, the dissipation is mainly due to frictional sliding.In the second part, we emphasize some remarkable features exhibited by dry grainavalanches in laboratory experiments. According to the slope angle, the rear frontpropagates either upwards or downwards, with velocity approximately equal to thedepth averaged velocity of the avalanche. As a counterpart, in both regimes, thevelocity magnitude of the head front remains of the order of twice the depthaveraged avalanche velocity. We suggest simple elementary mechanisms capable ofaccounting for these observations. We propose then an analytical modelling aimed atdescribing the combined processes governing the avalanche expansion. The twosolutions that we obtain for the growth regimes and for the avalanche shapesresemble very closely the observations made in the laboratory and in the field.