7 research outputs found
Response of a Hexagonal Granular Packing under a Localized External Force: Exact Results
We study the response of a two-dimensional hexagonal packing of massless,
rigid, frictionless spherical grains due to a vertically downward point force
on a single grain at the top layer. We use a statistical approach, where each
mechanically stable configuration of contact forces is equally likely. We show
that this problem is equivalent to a correlated -model. We find that the
response is double-peaked, where the two peaks, sharp and single-grain diameter
wide, lie on the two downward lattice directions emanating from the point of
the application of the external force. For systems of finite size, the
magnitude of these peaks decreases towards the bottom of the packing, while
progressively a broader, central maximum appears between the peaks. The
response behaviour displays a remarkable scaling behaviour with system size
: while the response in the bulk of the packing scales as , on
the boundary it is independent of , so that in the thermodynamic limit only
the peaks on the lattice directions persist. This qualitative behaviour is
extremely robust, as demonstrated by our simulation results with different
boundary conditions. We have obtained expressions of the response and higher
correlations for any system size in terms of integers corresponding to an
underlying discrete structure.Comment: Accepted for publication in JStat; 33 pages, 10 figures; Section 2.2
reorganized and rewritten; Details about the simulation procedure added in
Sec.3.1. ; A new section, summarizing the final results and the calculation
procedure adde
Sensitivity of the stress response function to packing preparation
A granular assembly composed of a collection of identical grains may pack
under different microscopic configurations with microscopic features that are
sensitive to the preparation history. A given configuration may also change in
response to external actions such as compression, shearing etc. We show using a
mechanical response function method developed experimentally and numerically,
that the macroscopic stress profiles are strongly dependent on these
preparation procedures. These results were obtained for both two and three
dimensions. The method reveals that, under a given preparation history, the
macroscopic symmetries of the granular material is affected and in most cases
significant departures from isotropy should be observed. This suggests a new
path toward a non-intrusive test of granular material constitutive properties.Comment: 15 pages, 11 figures, some numerical data corrected, to appear in J.
Phys. Cond. Mat. special issue on Granular Materials (M. Nicodemi Editor
Elasticity from the Force Network Ensemble in Granular Media
Transmission of forces in static granular materials are studied within the
framework of the force network ensemble, by numerically evaluating the
mechanical response of hexagonal packings of frictionless grains and
rectangular packings of frictional grains. In both cases, close to the point of
application of the overload, the response is non-linear and displays two peaks,
while at larger length-scales it is linear and elastic-like. The cross-over
between these two behaviors occurs at a depth that increases with the magnitude
of the overload, and decreases with increasing friction.Comment: 4 pages, 5 figures, accepted for Phys. Rev. Let
Clustering in a one-dimensional inelastic lattice gas
We analyze a lattice model closely related to the one-dimensional inelastic
gas with periodic boundary condition. The one-dimensional inelastic gas tends
to form high density clusters of particles with almost the same velocity,
separated by regions of low density; plotted as a function of particle indices,
the velocities of the gas particles exhibit sharp gradients, which we call
shocks. Shocks and clusters are seen to form in the lattice model too, although
no true positions of the particles are taken into account. The locations of the
shocks in terms of the particle index show remarkable independence on the
coefficient of restitution and the sequence of collisions used to update the
system, but they do depend on the initial configuration of the particle
velocities. We explain the microscopic origin of the shocks. We show that
dynamics of the velocity profile inside a cluster satisfies a simple continuum
equation, thereby allowing us to study cluster-cluster interactions at late
times.Comment: 8 pages, 7 figures, submitted to Phys. Rev.