Abstract: We use an analogy with the statistical mechanics of gas to
build the statistical mechanics of granular media. The case of an isotropic
disordered packing of equal spheres submitted to an isotropic stress is
considered. We use the assumption of a maximal disorder and the method of the
Lagrange multipliers to demonstrate that the distribution of the force moduli
decreases exponentially and obeys an exponential-decay statistics. This
distribution results from the above hypotheses and from the existence of a mean
stress, which acts as a constraint. This distribution is confirmed by
experiments and simulations. We apply the same method to find the distribution
of void defects of a granular assembly. It follows also an exponential-decay
statistics.
poudres & grains 9, 13-19 (15 novembre 1999)