909 research outputs found
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
Rheology and Contact Lifetime Distribution in Dense Granular Flows
We study the rheology and distribution of interparticle contact lifetimes for
gravity-driven, dense granular flows of non-cohesive particles down an inclined
plane using large-scale, three dimensional, granular dynamics simulations.
Rather than observing a large number of long-lived contacts as might be
expected for dense flows, brief binary collisions predominate. In the hard
particle limit, the rheology conforms to Bagnold scaling, where the shear
stress is quadratic in the strain rate. As the particles are made softer,
however, we find significant deviations from Bagnold rheology; the material
flows more like a viscous fluid. We attribute this change in the collective
rheology of the material to subtle changes in the contact lifetime distribution
involving the increasing lifetime and number of the long-lived contacts in the
softer particle systems.Comment: 4 page
Indeterminacy, Memory, and Motion in a Simple Granular Packing
We apply two theoretical and two numerical methods to the problem of a disk
placed in a groove and subjected to gravity and a torque. Methods assuming
rigid particles are indeterminate -- certain combinations of forces cannot be
calculated, but only constrained by inequalities. In methods assuming
deformable particles, these combinations of forces are determined by the
history of the packing. Thus indeterminacy in rigid particles becomes memory in
deformable ones. Furthermore, the torque needed to rotate the particle was
calculated. Two different paths to motion were identified. In the first,
contact forces change slowly, and the indeterminacy decreases continuously to
zero, and vanishes precisely at the onset of motion, and the torque needed to
rotate the disk is independent of method and packing history. In the second
way, this torque depends on method and on the history of the packing, and the
forces jump discontinuously at the onset of motion.Comment: 11 pages, 7 figures, submitted to Phys Rev
Piling and avalanches of magnetized particles
We performed computer simulations based on a two-dimensional Distinct Element
Method to study granular systems of magnetized spherical particles. We measured
the angle of repose and the surface roughness of particle piles, and we studied
the effect of magnetization on avalanching. We report linear dependence of both
angle of repose and surface roughness on the ratio of the magnetic dipole
interaction and the gravitational force (\emph{interparticle force ratio}).
There is a difference in avalanche formation at small and at large
interparticle force ratios. The transition is at . For
the particles forming the avalanches leave the system in a quasi-continuous
granular flow (\emph{granular regime}), while for the avalanches are
formed by long particle clusters (\emph{correlated regime}). The transition is
not sharp. We give plausible estimates for based on stability criteria.Comment: 9 pages, 7 figure
Mechanism for Surface Waves in Vibrated Granular Material
We use molecular dynamics simulations to study the formation of surface waves
in vertically vibrated granular material. We find that horizontal movements of
particles, which are essential for the formation of the waves, consist of two
distinct processes. First, the movements sharply increase while the particles
are colliding with a bottom plate, where the duration of the collisions is very
short compared to the period of the vibration. Next, the movements gradually
decrease between the collisions, during which the particles move through the
material. We also find that the horizontal velocity field after the collisions
is strongly correlated to the surface profile before the collisions.Comment: 6 pages, 3 figures (included
Measurements of the Yield Stress in Frictionless Granular Systems
We perform extensive molecular dynamics simulations of 2D frictionless
granular materials to determine whether these systems can be characterized by a
single static yield shear stress. We consider boundary-driven planar shear at
constant volume and either constant shear force or constant shear velocity.
Under steady flow conditions, these two ensembles give similar results for the
average shear stress versus shear velocity. However, near jamming it is
possible that the shear stress required to initiate shear flow can differ
substantially from the shear stress required to maintain flow. We perform
several measurements of the shear stress near the initiation and cessation of
flow. At fixed shear velocity, we measure the average shear stress
in the limit of zero shear velocity. At fixed shear force, we
measure the minimum shear stress required to maintain steady flow
at long times. We find that in finite-size systems ,
which implies that there is a jump discontinuity in the shear velocity from
zero to a finite value when these systems begin flowing at constant shear
force. However, our simulations show that the difference , and thus the discontinuity in the shear velocity, tend to zero in
the infinite system size limit. Thus, our results indicate that in the large
system limit, frictionless granular systems are characterized by a single
static yield shear stress. We also monitor the short-time response of these
systems to applied shear and show that the packing fraction of the system and
shape of the velocity profile can strongly influence whether or not the shear
stress at short times overshoots the long-time average value.Comment: 7 pages and 6 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
Amorphous Systems in Athermal, Quasistatic Shear
We present results on a series of 2D atomistic computer simulations of
amorphous systems subjected to simple shear in the athermal, quasistatic limit.
The athermal quasistatic trajectories are shown to separate into smooth,
reversible elastic branches which are intermittently broken by discrete
catastrophic plastic events. The onset of a typical plastic event is studied
with precision, and it is shown that the mode of the system which is
responsible for the loss of stability has structure in real space which is
consistent with a quadrupolar source acting on an elastic matrix. The plastic
events themselves are shown to be composed of localized shear transformations
which organize into lines of slip which span the length of the simulation cell,
and a mechanism for the organization is discussed. Although within a single
event there are strong spatial correlations in the deformation, we find little
correlation from one event to the next, and these transient lines of slip are
not to be confounded with the persistent regions of localized shear --
so-called "shear bands" -- found in related studies. The slip lines gives rise
to particular scalings with system length of various measures of event size.
Strikingly, data obtained using three differing interaction potentials can be
brought into quantitative agreement after a simple rescaling, emphasizing the
insensitivity of the emergent plastic behavior in these disordered systems to
the precise details of the underlying interactions. The results should be
relevant to understanding plastic deformation in systems such as metallic
glasses well below their glass temperature, soft glassy systems (such as dense
emulsions), or compressed granular materials.Comment: 21 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
Shear strength properties of wet granular materials
We investigate shear strength properties of wet granular materials in the
pendular state (i.e. the state where the liquid phase is discontinuous) as a
function of water content. Sand and glass beads were wetted and tested in a
direct shear cell and under various confining pressures. In parallel, we
carried out three-dimensional molecular dynamics simulations by using an
explicit equation expressing capillary force as a function of interparticle
distance, water bridge volume and surface tension. We show that, due to the
peculiar features of capillary interactions, the major influence of water
content over the shear strength stems from the distribution of liquid bonds.
This property results in shear strength saturation as a function of water
content. We arrive at the same conclusion by a microscopic analysis of the
shear strength. We propose a model that accounts for the capillary force, the
granular texture and particle size polydispersity. We find fairly good
agreement of the theoretical estimate of the shear strength with both
experimental data and simulations. From numerical data, we analyze the
connectivity and anisotropy of different classes of liquid bonds according to
the sign and level of the normal force as well as the bond direction. We find
that weak compressive bonds are almost isotropically distributed whereas strong
compressive and tensile bonds have a pronounced anisotropy. The probability
distribution function of normal forces is exponentially decreasing for strong
compressive bonds, a decreasing power-law function over nearly one decade for
weak compressive bonds and an increasing linear function in the range of
tensile bonds. These features suggest that different bond classes do not play
the same role with respect to the shear strength.Comment: 12 page
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