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The European Physical Journal E

, Volume 7, Issue 4, pp 353–370 | Cite as

Directed force chain networks and stress response in static granular materials

  • J.E.S. Socolar
  • D.G. Schaeffer
  • P. Claudin
Article

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 

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Copyright information

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

Authors and Affiliations

  • J.E.S. Socolar
    • 1
  • D.G. Schaeffer
    • 2
  • P. Claudin
    • 3
  1. 1.Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708, USADurhamUSA
  2. 2.Department of Mathematics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708, USADurhamUSA
  3. 3.Laboratoire des Milieux Désordonnés et Hétérogènes (UMR 7603), 4 place Jussieu, case 86, 75252 Paris Cedex 05, FranceParis CedexFrance

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