Statistical theories for the elastic moduli of two-dimensional assemblies of granular materials

In this micro-mechanical study of the behaviour of granular materials, a minimum potential energy and a minimum complementary energy principle are derived for the elastic moduli of two-dimensional, bonded assemblies of particles, These extremum principles are used to obtain bounds on the elastic moduli. Statistical versions of these energy principles are developed. The theoretical results are verified by computer simulations using the discrete element method. Good agreement between theory and simulations is observed. (C) 1998 Elsevier Science Ltd. All rights reserved.