37 research outputs found
Stress response function of a two-dimensional ordered packing of frictional beads
We study the stress profile of an ordered two-dimensional packing of beads in
response to the application of a vertical overload localized at its top
surface. Disorder is introduced through the Coulombic friction between the
grains which gives some indeterminacy and allows the choice of one constrained
random number per grain in the calculation of the contact forces. The so-called
`multi-agent' technique we use, lets us deal with systems as large as
grains. We show that the average response profile has a double
peaked structure. At large depth , the position of these peaks grows with
, while their widths scales like . and are analogous to
`propagation' and `diffusion' coefficients. Their values depend on that of the
friction coefficient . At small , we get and , with , which means that the peaks get
closer and wider as the disorder gets larger. This behavior is qualitatively
what was predicted in a model where a stochastic relation between the stress
components is assumed.Comment: 7 pages, 7 figures, accepted version to Europhys. Let
Force distributions in 3D granular assemblies: Effects of packing order and inter-particle friction
We present a systematic investigation of the distribution of normal forces at
the boundaries of static packings of spheres. A new method for the efficient
construction of large hexagonal-close-packed crystals is introduced and used to
study the effect of spatial ordering on the distribution of forces. Under
uniaxial compression we find that the form for the probability distribution of
normal forces between particles does not depend strongly on crystallinity or
inter-particle friction. In all cases the distribution decays exponentially at
large forces and shows a plateau or possibly a small peak near the average
force but does not tend to zero at small forces.Comment: 9 pages including 8 figure
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
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