Stress response function of a twodimensional ordered packing of frictional beads
Abstract
We study the stress profile of an ordered twodimensional packing of beads in response to the application of a vertical overload localized at its top surface. Disorder is introduced through the Coulombic friction between the grains which gives some indeterminacy and allows the choice of one constrained random number per grain in the calculation of the contact forces. The socalled "multiagent" technique we use lets us deal with systems as large as 1000 × 1000 grains. We show that the average response profile has a doublepeaked structure. At large depth z, the position of these peaks grows with cz, while their widths scales like √Dz. c and D are analogous to "propagation" and "diffusion" coefficients. Their values depend on that of the friction coefficient μ. At small μ, we get c_{0}  c propto μ and D propto μ^{β}, with β ~ 2.5, which means that the peaks get closer and wider as the disorder gets larger. This behavior is qualitatively what was predicted in a model where a stochastic relation between the stress components is assumed.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 December 2002
 DOI:
 10.1209/epl/i2002003096
 arXiv:
 arXiv:condmat/0205089
 Bibcode:
 2002EL.....60..813B
 Keywords:

 05.40.a;
 45.70.Cc;
 83.80.Fg;
 Fluctuation phenomena random processes noise and Brownian motion;
 Static sandpiles;
 granular compaction;
 Granular solids;
 Condensed Matter
 EPrint:
 7 pages, 7 figures, accepted version to Europhys. Lett