5 research outputs found
Directed force chain networks and stress response in static granular materials
A theory of stress fields in two-dimensional granular materials based on
directed force chain networks is presented. A general equation for the
densities of force chains in different directions is proposed and a complete
solution is obtained for a special case in which chains lie along a discrete
set of directions. The analysis and results demonstrate the necessity of
including nonlinear terms in the equation. A line of nontrivial fixed point
solutions is shown to govern the properties of large systems. In the vicinity
of a generic fixed point, the response to a localized load shows a crossover
from a single, centered peak at intermediate depths to two propagating peaks at
large depths that broaden diffusively.Comment: 18 pages, 12 figures. Minor corrections to one figur
Force distribution in a scalar model for non-cohesive granular material
We study a scalar lattice model for inter-grain forces in static,
non-cohesive, granular materials, obtaining two primary results. (i) The
applied stress as a function of overall strain shows a power law dependence
with a nontrivial exponent, which moreover varies with system geometry. (ii)
Probability distributions for forces on individual grains appear Gaussian at
all stages of compression, showing no evidence of exponential tails. With
regard to both results, we identify correlations responsible for deviations
from previously suggested theories.Comment: 16 pages, 9 figures, Submitted to PR
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