20 research outputs found
Stresses in isostatic granular systems and emergence of force chains
Progress is reported on several questions that bedevil understanding of
granular systems: (i) are the stress equations elliptic, parabolic or
hyperbolic? (ii) how can the often-observed force chains be predicted from a
first-principles continuous theory? (iii) How to relate insight from isostatic
systems to general packings? Explicit equations are derived for the stress
components in two dimensions including the dependence on the local structure.
The equations are shown to be hyperbolic and their general solutions, as well
as the Green function, are found. It is shown that the solutions give rise to
force chains and the explicit dependence of the force chains trajectories and
magnitudes on the local geometry is predicted. Direct experimental tests of the
predictions are proposed. Finally, a framework is proposed to relate the
analysis to non-isostatic and more realistic granular assemblies.Comment: 4 pages, 2 figures, Corrected typos and clkearer text, submitted to
Phys. Rev. Let
Stress in frictionless granular material: Adaptive Network Simulations
We present a minimalistic approach to simulations of force transmission
through granular systems. We start from a configuration containing cohesive
(tensile) contact forces and use an adaptive procedure to find the stable
configuration with no tensile contact forces. The procedure works by
sequentially removing and adding individual contacts between adjacent beads,
while the bead positions are not modified. In a series of two-dimensional
realizations, the resulting force networks are shown to satisfy a linear
constraint among the three components of average stress, as anticipated by
recent theories. The coefficients in the linear constraint remain nearly
constant for a range of shear loadings up to about .6 of the normal loading.
The spatial distribution of contact forces shows strong concentration along
``force chains". The probability of contact forces of magnitude f shows an
exponential falloff with f. The response to a local perturbing force is
concentrated along two characteristic rays directed downward and laterally.Comment: 8 pages, 8 figure
Stress Propagation through Frictionless Granular Material
We examine the network of forces to be expected in a static assembly of hard,
frictionless spherical beads of random sizes, such as a colloidal glass. Such
an assembly is minimally connected: the ratio of constraint equations to
contact forces approaches unity for a large assembly. However, the bead
positions in a finite subregion of the assembly are underdetermined. Thus to
maintain equilibrium, half of the exterior contact forces are determined by the
other half. We argue that the transmission of force may be regarded as
unidirectional, in contrast to the transmission of force in an elastic
material. Specializing to sequentially deposited beads, we show that forces on
a given buried bead can be uniquely specified in terms of forces involving more
recently added beads. We derive equations for the transmission of stress
averaged over scales much larger than a single bead. This derivation requires
the Ansatz that statistical fluctuations of the forces are independent of
fluctuations of the contact geometry. Under this Ansatz, the
-component stress field can be expressed in terms of a d-component
vector field. The procedure may be generalized to non-sequential packings. In
two dimensions, the stress propagates according to a wave equation, as
postulated in recent work elsewhere. We demonstrate similar wave-like
propagation in higher dimensions, assuming that the packing geometry has
uniaxial symmetry. In macroscopic granular materials we argue that our approach
may be useful even though grains have friction and are not packed
sequentially.=17Comment: 15 pages, 4 figures, revised vertion for Phys. Rev.