This article has an erratum: [https://doi.org/10.1140/epje/i2002-10030-4]

Eur. Phys. J. E 7, 353-370 (2002)
DOI: 10.1140/epje/i2002-10011-7

Directed force chain networks and stress response in static granular materials

J.E.S. Socolar¹, D.G. Schaeffer² and P. Claudin<sup>3

1</sup>  Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708, USA
²  Department of Mathematics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708, USA
³  Laboratoire des Milieux Désordonnés et Hétérogènes (UMR 7603), 4 place Jussieu, case 86, 75252 Paris Cedex 05, France

(Received 16 January 2002)

Erratum

Abstract
A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general Boltzmann 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 Boltzmann 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.

PACS
45.70.Cc - Static sandpiles; granular compaction.
83.80.Fg - Granular solids.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002