533 research outputs found
Simulated three-component granular segregation in a rotating drum
Discrete particle simulations are used to model segregation in granular
mixtures of three different particle species in a horizontal rotating drum.
Axial band formation is observed, with medium-size particles tending to be
located between alternating bands of big and small particles. Partial radial
segregation also appears; it precedes the axial segregation and is
characterized by an inner core region richer in small particles. Axial bands
are seen to merge during the long simulation runs, leading to a coarsening of
the band pattern; the relocation of particles involved in one such merging
event is examined. Overall, the behavior is similar to experiment and
represents a generalization of what occurs in the simpler two-component
mixture.Comment: 7 pages, 11 figures (low resolution color figures only; originals at
author's website http://www.ph.biu.ac.il/~rapaport/research/granular.html)
[revised version contains extra figures
Granular Packings: Nonlinear elasticity, sound propagation and collective relaxation dynamics
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
experiments, numerical simulations and theoretical studies to understand the
elastic response of a deforming granular assembly of soft spheres under
isotropic loading. Our results for the behavior of the elastic moduli of the
system agree very well with experiments. We show that the elasticity partially
describes the experimental and numerical results for a system under
compressional loads. However, it drastically fails for systems under shear
perturbations, particularly for packings without tangential forces and
friction. Our work indicates that a correct treatment should include not only
the purely elastic response but also collective relaxation mechanisms related
to structural disorder and nonaffine motion of grains.Comment: 21 pages, 13 figure
Scale separation in granular packings: stress plateaus and fluctuations
It is demonstrated, by numerical simulations of a 2D assembly of polydisperse
disks, that there exists a range (plateau) of coarse graining scales for which
the stress tensor field in a granular solid is nearly resolution independent,
thereby enabling an `objective' definition of this field. Expectedly, it is not
the mere size of the the system but the (related) magnitudes of the gradients
that determine the widths of the plateaus. Ensemble averaging (even over
`small' ensembles) extends the widths of the plateaus to sub-particle scales.
The fluctuations within the ensemble are studied as well. Both the response to
homogeneous forcing and to an external compressive localized load (and gravity)
are studied. Implications to small solid systems and constitutive relations are
briefly discussed.Comment: 4 pages, 4 figures, RevTeX 4, Minor corrections to match the
published versio
Effective boundary conditions for dense granular flows
We derive an effective boundary condition for granular flow taking into
account the effect of the heterogeneity of the force network on sliding
friction dynamics. This yields an intermediate boundary condition which lies in
the limit between no-slip and Coulomb friction; two simple functions relating
wall stress, velocity, and velocity variance are found from numerical
simulations. Moreover, we show that this effective boundary condition
corresponds to Navier slip condition when GDR MiDi's model is assumed to be
valid, and that the slip length depends on the length scale that characterises
the system, \emph{viz} the particle diameter.Comment: 4 pages, 5 figure
Microscopic origin of granular ratcheting
Numerical simulations of assemblies of grains under cyclic loading exhibit
``granular ratcheting'': a small net deformation occurs with each cycle,
leading to a linear accumulation of deformation with cycle number. We show that
this is due to a curious property of the most frequently used models of the
particle-particle interaction: namely, that the potential energy stored in
contacts is path-dependent. There exist closed paths that change the stored
energy, even if the particles remain in contact and do not slide. An
alternative method for calculating the tangential force removes granular
ratcheting.Comment: 13 pages, 18 figure
Phase transition in inelastic disks
This letter investigates the molecular dynamics of inelastic disks without
external forcing. By introducing a new observation frame with a rescaled time,
we observe the virtual steady states converted from asymptotic energy
dissipation processes. System behavior in the thermodynamic limit is carefully
investigated. It is found that a phase transition with symmetry breaking occurs
when the magnitude of dissipation is greater than a critical value.Comment: 9 pages, 6 figure
Why Effective Medium Theory Fails in Granular Materials
Experimentally it is known that the bulk modulus, K, and shear modulus, \mu,
of a granular assembly of elastic spheres increase with pressure, p, faster
than the p^1/3 law predicted by effective medium theory (EMT) based on
Hertz-Mindlin contact forces. To understand the origin of these discrepancies,
we perform numerical simulations of granular aggregates under compression. We
show that EMT can describe the moduli pressure dependence if one includes the
increasing number of grain-grain contacts with p. Most important, the affine
assumption (which underlies EMT), is found to be valid for K(p) but breakdown
seriously for \mu(p). This explains why the experimental and numerical values
of \mu(p) are much smaller than the EMT predictions.Comment: 4 pages, 5 figures, http://polymer.bu.edu/~hmaks
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