Statistics of the elastic behaviour of granular materials

The elastic behaviour of isotropic assemblies of granular materials consist ing of two-dimensional, bonded and nonrotating particles is studied from th e micromechanical viewpoint. Discrete element simulations have been perform ed of assemblies of 50,000 particles with various coordination numbers (ave rage number of contacts per particle) and various ratios of tangential to n ormal stiffness. Statistics, such as mean, standard deviation and probabili ty distribution function, have been computed for geometrical quantities and contact displacements under compressive and shearing loading. A linear rel ation is observed between the average number of contacts of a particle and its circumference. Average displacements do not conform to (generalised) un iform strain as is often assumed. The probability density functions for nor mal and tangential displacements are nearly Gaussian. None of the considere d energies satisfy an equipartition of energy between normal and tangential modes. (C) 2001 Elsevier Science Ltd. All rights reserved.