Reply to "Comment on mechanical analog of temperature for the description of force distribution in static granular packings"

Abstract

Metzger [preceding paper, Phys. Rev. E 69, 053301 (2004)] put forward a number of arguments against the Gaussian force distribution concluded in the investigations by Ngan [ Phys. Rev. E 68, 011301 (2003) ] and by some previous workers. It is shown here that, with a more proper choice for the constraint in the free energy minimization, the Shannon entropy approach can predict three-dimensional force distributions that are in much better agreement with simulated distributions. In two-dimensional packings, if one accepts a Gaussian distribution at some finite strain in a Hookean force-law situation, then the superposition principle of linear elasticity predicts that the same Gaussian distribution will be maintained at vanishing strains. This argument forms an interesting dilemma with Metzger's argument about the noninvolvement of the force law in statically determinate packings.