Eur. Phys. J. E 7, 353-370 (2002)
Directed force chain networks and stress response in static granular materialsJ.E.S. Socolar1, D.G. Schaeffer2 and P. Claudin3
1 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)
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.
45.70.Cc - Static sandpiles; granular compaction.
83.80.Fg - Granular solids.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002