1208.0252 (Ignacio G. Tejada)

Stress phase space for static granular matter    [PDF]

Ignacio G. Tejada

Some statistical mechanics approaches to jammed granular media are based on ensembles in which the stress state of the system is externally set. This paper proposes a new phase space to describe the microstates of a granular packing compatible to a given macrostate. The nature of this phase space is analyzed, showing that the consideration of the allowed and forbidden regions of every configuration (i.e. geometrical pattern) could be a relevant factor for the establishment of its probability and, therefore, of the expected properties of the sample. Many combinations of forces acting on a particle can keep it in static equilibrium. Every set of forces could be considered equivalent to a microscopic stress field, but the kind of interaction and the geometrical restrictions mean that not all stress states can be represented by any set. Consequently every local configuration has its respective allowed and forbidden regions in the phase space. As a result, some points of the phase space are degenerate, and the density of states strongly determines the expected statistical distribution in the thermodynamic equilibrium. It is shown how this function just depends on the deviatoric stress. A first analysis of two-dimensional (2D) arrangements is included to clarify this assertion.

View original: http://arxiv.org/abs/1208.0252