Statistics of the Elastic Behavior of Granular Materials

The elastic behaviour of isotropic assemblies of granular materials consisting of two-dimensional, bonded and non-rotating particles is studied from the micromechanical viewpoint. Discrete element simulations have been performed of assemblies of 50,000 particles with various coordination numbers (average number of contacts per particle) and various ratios of tangential to normal stiffness. Statistics, such as mean, standard deviation and probability distribution function, have been computed for geometrical quantities and contact displacements under compressive and shearing loading. A linear relation is observed between the average number of contacts of a particle and its circumference. Average displacements do not conform to (generalised) uniform strain as is often assumed. The probability density functions for normal and tangential displacements are nearly Gaussian. None of the considered energies satisfy an equipartition of energy between normal and tangential modes.