Force transmission in granular materials involves two key aspects that have generally been treated separately: (1) the broad probability density function of force magnitudes, and (2) the anisotropic distribution of contact orientations and the forces they transmit. In this paper, we first analyze the origins of the exponential distribution of strong forces and the non-exponential behavior observed in the weak-force range. We show that the exponential tail arises naturally from the statistical independence of contact forces acting on each particle, a consequence of the inherent disorder in granular packings. We then introduce a self-consistent force model for isotropic systems with a single free parameter that accounts for the non-exponential behavior of weak forces. We extend this model to account for both fabric and force anisotropies. We show that the resulting anisotropic force distribution successfully captures the bimodal nature of force transmission, as well as the dependence of the force statistics on the underlying fabric and force anisotropies.
Radjai et al. (Mon,) studied this question.
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