On the distribution of elastic forces in disordered structures and materials. II A statistical mechanics theory

Abstract

Based on computer simulated results in prototypical examples of granular packings and random open-cell foams in part I of the present study, a theoretical framework based on statistical physics concepts is developed in this work to describe the internal force distributions in random materials under external loadings. The theory involves the use of an entropy functional to represent the effect of structural randomness on the force distribution, and this is assumed to remain constant during energy minimization in the search of equilibrium states. The theory accurately predicts the form of the force distributions obtained by computer simulations up to an unknown parameter, which is analogous to the temperature in a thermal system. The predicted internal force distributions can be used to construct failure surfaces based on a first-yield criterion. © 2005 The Royal Society.