Stress phase space for static granular matter

This paper proposes a phase space to compare the static packings of a granular system compatible to a macrostate that is set by the external stress. The nature of this phase space is analyzed, showing that the consideration of the allowed and forbidden regions and the internal degrees of freedom 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. This is due to the fact that many combinations of forces acting on a particle can keep it in static equilibrium. Every set of forces can 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, whereas others can be represented by many sets. Consequently the points of the phase space are degenerate, and the density of states of each configuration strongly determines the most probable statistical distribution. It is shown how these functions just depend on the deviatoric stress. A first analysis of two-dimensional (2D) arrangements is included to clarify this assertion.