Mechanical analog of temperature for the description of force distribution in static granular packings

It is shown that in a stressed granular packing, the effect of the applied pressure and structural randomness on the contact force distribution can be described accurately by a variational principle of minimizing energy subject to the constraint of keeping entropy at a fixed value. The constraint on entropy may be regarded as a measure of the degree of retained disorderness in the system. This procedure leads to the introduction of a parameter known as the "mechanical temperature." Similar to the role of the conventional thermal temperature in a thermal system, the mechanical temperature can be viewed as a parameter controlling the mixity between energy minimization and entropy maximization in the equilibrium condition.