Distribution of contact forces in a homogeneous
granular material of identical spheres under triaxial compression

P.
Evesque: Lab MSSM, UMR 8579 CNRS, Ecole Centrale Paris, 92295 Châtenay-Malabry,
France , **evesque@mssmat.ecp.fr**

**Abstract: **The
study of the distribution ρ(f)
of contact forces F in a homogeneous isotropic disordered granular sample
subject to uniform triaxial stress field is undertaken using a model where
forces propagate and collide. Collisions occur at grain and obey given rules
which allow satisfying local static equilibrium. Analogy with Boltzmann’s
equation of density evolution is drawn and used to derive the parameters that
control the distribution ρ_{s}(f)
of contact forces F in the stationary state in case of a packing of
mono-disperse spheres. Using symmetry argument and mean field approximation, it
is found that stationarity is achieved when the density ρ_{s}(f)
of force can be written as the product of exponentials of quantities whose sums
are preserved during collisions. This introduces 3 parameters in 2d and 6 in 3d
which are the mean force components {F_{xo}, F_{yo} , F_{zo}
}, and the mean torques of the force on a grain {M_{xo}, M_{yo}
, M_{zo}} . Astonishingly, it seems that the theory cannot include
distribution of contact orientation implicitly. Extension of the model is
possible with some care to case of anisotropic packing.

**Pacs # :** 5.40 ; 45.70 ; 62.20 ; 83.70.Fn* *

*poudres & grains ***14 **(4), 82-95
(2004)