Eur. Phys. J. E 4, 451-457
Force chain splitting in granular materials: A mechanism for large-scale pseudo-elastic behaviour
J.-P. Bouchaud1, P. Claudin2, D. Levine2 and M. Otto11 Service de Physique de l'Etat Condensé, CEA-Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
2 Technion - Israel Institute of Technology, Physics Department, Haifa 32000, Israel
bouchau@spec.saclay.cea.fr
(Received 13 November 2000 and Received in final form 3 January 2001)
Abstract
We investigate both numerically and analytically the effect of strong
disorder on the large-scale properties of the hyperbolic equations
for stresses proposed in J.-P. Bouchaud, M.E. Cates, P. Claudin,
J. Phys. I 5, 639 (1995), and
J.P. Wittmer, P. Claudin, M.E. Cates, J.-P. Bouchaud,
Nature 382, 336 (1996);
J.P. Wittmer, P. Claudin, M.E. Cates,
J. Phys. I 7, 39 (1997).
The physical mechanism that
we model is the local splitting of the force chains (the characteristics
of the hyperbolic equation) by packing defects. In analogy with the theory
of light diffusion in a turbid medium, we propose a Boltzmann-like equation
to describe these processes. We show that, for isotropic packings, the
resulting large-scale effective equations for the stresses have exactly the
same structure as those of an elastic body, despite the fact that no
displacement field needs to be introduced at all. Correspondingly, the
response function evolves from a two-peak structure at short scales to a
broad hump at large scales. We find, however, that the Poisson ratio is
anomalously large and incompatible with classical elasticity theory that
requires the reference state to be thermodynamically stable.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
45.70.Cc - Static sandpiles; granular compaction.
83.70.Fn - Granular solids.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001
