title: Directed force chain networks and stress response in static granular materials.
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.
authors.affiliation: Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708, USA, Durham, USA.
authors.forename: J E S
authors.initials: JE
authors.lastname: Socolar
authors.affiliation: Department of Mathematics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708, USA, Durham, USA.
authors.forename: D G
authors.initials: DG
authors.lastname: Schaeffer
authors.affiliation: Laboratoire des Milieux Désordonnés et Hétérogènes (UMR 7603), 4 place Jussieu, case 86, 75252 Paris Cedex 05, France, Paris Cedex, France.
authors.forename: P
authors.initials: P
authors.lastname: Claudin
keywords: PACS. 45.70.Cc Static sandpiles; granular compaction – 83.80.Fg Granular solids