A new statistical mechanics approach to dense granular media

A new statistical mechanics approach to dense granular media is presented. The thermodynamic formalism is set out directly in terms of elastic potential energy, such that the configurational temperature (the intensive property which defines the steady state) relates to a quadratic function of the stresses (rather than other linear functions used in recent developments). Dense granular media are considered as canonical ensembles of noninteracting clusters, which can be identified with repeatable equilibrium configurations. Then, particles can be located in a new proposed phase space (conceived to separate the elastic potential energy levels). Although the importance of this paper lies in the method itself, it has been illustratively applied to the simple case of two-dimensional (2D) dense granular media (an arrangement of frictionless monodisperse elastic disks under isotropic horizontal stress compression). In this case, the temperature is directly replaced by the squared external pressure, and the packing ratio of the most probable microstate is close to the reported value of random close packing. Moreover, some interesting general conclusions arise.