Math @ Duke

Publications [#244133] of David G. Schaeffer
Papers Published
 Socolar, JES; Schaeffer, DG; Claudin, P, Directed force chain networks and stress response in static granular materials,
European Physical Journal E, vol. 7 no. 4
(2002),
pp. 353370
(last updated on 2017/12/12)
Abstract: A theory of stress fields in twodimensional 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 fixedpoint 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.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

