3 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
Anisotropy in granular media: classical elasticity and directed force chain network
A general approach is presented for understanding the stress response
function in anisotropic granular layers in two dimensions. The formalism
accommodates both classical anisotropic elasticity theory and linear theories
of anisotropic directed force chain networks. Perhaps surprisingly, two-peak
response functions can occur even for classical, anisotropic elastic materials,
such as triangular networks of springs with different stiffnesses. In such
cases, the peak widths grow linearly with the height of the layer, contrary to
the diffusive spreading found in `stress-only' hyperbolic models. In principle,
directed force chain networks can exhibit the two-peak, diffusively spreading
response function of hyperbolic models, but all models in a particular class
studied here are found to be in the elliptic regime.Comment: 34 pages, 17 figures (eps), submitted to PRE, figures amended,
partially to compare better to recent exp. wor
Stress response inside perturbed particle assemblies
The effect of structural disorder on the stress response inside three
dimensional particle assemblies is studied using computer simulations of
frictionless sphere packings. Upon applying a localised, perturbative force
within the packings, the resulting {\it Green's} function response is mapped
inside the different assemblies, thus providing an explicit view as to how the
imposed perturbation is transmitted through the packing. In weakly disordered
arrays, the resulting transmission of forces is of the double-peak variety, but
with peak widths scaling linearly with distance from the source of the
perturbation. This behaviour is consistent with an anisotropic elasticity
response profile. Increasing the disorder distorts the response function until
a single-peak response is obtained for fully disordered packings consistent
with an isotropic description.Comment: 8 pages, 7 figure captions To appear in Granular Matte