Stresses in smooth flows of dense granular media

Depken, Martin; Lechman, Jeremy B.; Hecke, Martin van; Saarloos, Wim van; Grest, Gary S.

doi:10.1209/0295-5075/78/58001

Cited by 57 publications

(87 citation statements)

References 20 publications

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“…This assertion is stronger than just coaxiality and has been presumed by some (39) while challenged by others (57). Our data reveals reasonably large variations from purely codirectional flow.…”

Section: Computation Of Materials Variablessupporting

confidence: 53%

Assessing continuum postulates in simulations of granular flow

Rycroft

Kamrin

Bazant

2009

Journal of the Mechanics and Physics of Solids

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Continuum mechanics relies on the fundamental notion of a mesoscopic volume "element" in which properties averaged over discrete particles obey deterministic relationships. Recent work on granular materials suggests a continuum law may be inapplicable, revealing inhomogeneities at the particle level, such as force chains and slow cage breaking. Here, we analyze large-scale three-dimensional Discrete-Element Method (DEM) simulations of different granular flows and show that an approximate "granular element" defined at the scale of observed dynamical correlations (roughly three to five particle diameters) has a reasonable continuum interpretation. By viewing all the simulations as an ensemble of granular elements which deform and move with the flow, we can track material evolution at a local level. Our results confirm some of the hypotheses of classical plasticity theory while contradicting others and suggest a subtle physical picture of granular failure, combining liquid-like dependence on deformation rate and solid-like dependence on strain. Our computational methods and results can be used to guide the development of more realistic continuum models, based on observed local relationships between average variables.Key words: granular materials, numerical methods * Corresponding author.Email addresses: chr@math.berkeley.edu (Chris H. Rycroft), kenman@mit.edu (Ken Kamrin), bazant@mit.edu (Martin Z. Bazant). Preprint submitted to Elsevier26 August 2008 Fig. 1. A typical 2.5d × 8d × 2.5d cell of particles from a DEM simulation, which forms the basis of the approximate granular element considered in this paper.

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Section: Computation Of Materials Variablessupporting

confidence: 53%

Assessing continuum postulates in simulations of granular flow

Rycroft

Kamrin

Bazant

2009

Journal of the Mechanics and Physics of Solids

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“…This simulation code is welldeveloped and has been used by many authors over a number of years [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. It employs a modified version of a contact model originally employed by Cundall and Strack [33] for the simulation of cohesionless particulates, featuring a normal elastic interaction, viscoelastic terms, history-dependent tangential forces and a Coulomb friction criterion.…”

Section: Introductionmentioning

confidence: 99%

Physical test of a particle simulation model in a sheared granular system

2009

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We report a detailed comparison of a slow gravity driven sheared granular flow with a computational model performed with the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). To our knowledge, this is the first thorough test of the LAMMPS model with a laboratory granular flow. In the experiments, grains flow inside a silo with a rectangular cross-section, and are sheared by a rough boundary on one side and smooth boundaries on the other sides. Individual grain position and motion are measured using a particle index matching imaging technique where a fluorescent dye is added to the interstitial liquid which has the same refractive index as the glass beads. The boundary imposes a packing order, and the grains are observed to flow in layers which get progressively more disordered with distance from the walls. The computations use a Cundall-Strack contact model between the grains, using contact parameters that have been used in many other previous studies, and ignore the hydrodynamic effects of the interstitial liquid. Computations are performed to understand the effect of particle coefficient of friction, elasticity, contact model, and polydispersity on mean flow properties. After appropriate scaling, we find that the mean velocity of the grains and the number density as a function of flow cross-section observed in the experiments and the simulations are in excellent agreement. The mean flow profile is observed to be unchanged over a broad range of coefficient of friction, except near the smooth wall. We show that the flow profile is not sensitive to at least 10% polydispersity in particle size. Because the grain elasticity used is smaller in the computations as compared with glass grains, wave-like features can be noted over short time scales in the mean velocity and the velocity auto-correlations measured in the simulations. These wave features occur over an intermediate timescale larger than the particle interaction but smaller than the timescale of the macroscopic flow features. The wave features become more prominent as grain elasticity is further reduced. We then perform a detailed comparison of the particle fluctuation properties as measured by the displacement probability distribution function and the mean square displacement. Excellent agreement is observed over a time interval over which particles can be tracked effectively in the experiments. Using the longer tracking intervals possible in the simulations, we find that the diffusion in the layers is greater in the flow direction, than in the perpendicular direction. Further signatures of confinement and hopping between layers is observed. All in all, our study provides strong support for the LAMMPS model of granular flow, and further supports the hypothesis that the interstitial liquid has negligible effects on granular fluctuations provided the flow is slow.

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“…Central to the model is a scalar state variable g, called the granular fluidity, which represents the susceptibility of a granular cluster to flow. Mathematically, it functions as a field variable that relates the load intensity µ to the consequent flow rateγ, i.e.,γ = gµ, so that the tensorial relation between the Cauchy stress and the strain rate iswhere we have made the common assumption that the strain-rate and deviatoric Cauchy stress tensors are codirectional [17,18,26], though this is an approximation [28,29]. In a local description of granular flow, the fluidity is constitutively given as a function of the stress, in a manner consistent with Bagnold scaling [30].…”

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confidence: 99%

“…where we have made the common assumption that the strain-rate and deviatoric Cauchy stress tensors are codirectional [17,18,26], though this is an approximation [28,29]. In a local description of granular flow, the fluidity is constitutively given as a function of the stress, in a manner consistent with Bagnold scaling [30].…”

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confidence: 99%

Continuum Modeling of Secondary Rheology in Dense Granular Materials

Henann

Kamrin

2014

Phys. Rev. Lett.

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Recently, a new nonlocal granular rheology was successfully used to predict steady granular flows, including grain-size-dependent shear features, in a wide variety of flow configurations, including all variations of the split-bottom cell. A related problem in granular flow is that of mechanicallyinduced creep, in which shear deformation in one region of a granular medium fluidizes its entirety, including regions far from the sheared zone, effectively erasing the yield condition everywhere. This enables creep deformation when a force is applied in the nominally quiescent region through an intruder such as a cylindrical or spherical probe. We show that the nonlocal fluidity model is capable of capturing this phenomenology. Specifically, we explore creep of a circular intruder in a two-dimensional annular Couette cell and show that the model captures all salient features observed in experiments, including both the rate-independent nature of creep for sufficiently slow driving rates and the faster-than-linear increase in the creep speed with the force applied to the intruder.Cooperativity is a hallmark of quasi-static, dense granular deformation. At a microscopic level, deformation in granular materials takes place through the rearrangement of clusters of grains. These rearrangement events lead to long-range fluctuations, or agitations, that influence the behavior of nearby clusters, leading to macroscopic manifestations of cooperativity, which are quite varied. Most familiarly, the length-scales associated with velocity fields in dense granular flows depend crucially upon the grain size [1], with grain-size dependent shear band widths being observed in many geometries [2][3][4][5][6][7][8]. Other manifestations of cooperativity include the dependence of volumetric outflow rate on grain size in drainage flows [9,10] and the so-called H stop -effect, in which thin granular layers require greater tilt to flow down an inclined surface [11,12]. A more recently-observed example of cooperativity in dense granular flows is that of mechanicallyinduced creep [13][14][15], understood as follows. When an intruder, such as a sphere, rod, or vane, is placed in a dense granular material, one must apply a force to the intruder that exceeds a critical value in order to move it through the granular media. However, shear deformation far from the intruder enables it to move, or creep, through the granular media for any non-zero value of the applied force -even when this force is less than the critical value. That is to say, flow anywhere in a granular media erases the yield condition everywhere! These cooperative phenomena provide stringent tests for a continuum model of granular flow. Local approaches to continuum modeling of granular materials, such as granular rheology [16][17][18] or soil mechanics [19,20], which relate the stress at a point to the local strain, strain-rate, or locally evolved state variables, are not equipped to address size-dependent manifestations of cooperativity. Recently, we proposed a nonlocal rheology for ...

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Stresses in smooth flows of dense granular media

Cited by 57 publications

References 20 publications

Assessing continuum postulates in simulations of granular flow

Assessing continuum postulates in simulations of granular flow

Physical test of a particle simulation model in a sheared granular system

Continuum Modeling of Secondary Rheology in Dense Granular Materials

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