Micromechanics of the elastic behaviour of granular materials

Micromechanics of granular materials deals with the relation between microscopic and macroscopic characteristics. This study focuses on elastic behaviour. An overview of micromechanics of granular materials is given. Two regimes are identified, uniform strain and uniform stress. It follows from extremum principles that these regimes correspond to upper and lower bounds for the moduli. A statistical theory is outlined that is based on maximum disorder. The results of Discrete Element simulations, based on isotropic assemblies of 50,000 particles, are used to gain insight in the relevant phenomena and to verify theoretical predictions. A linear relation between number of contacts and particle radius is observed. The statistical theory is valid for loose systems, while the uniform strain theory is valid for dense systems. In general, the relative displacements do not match the uniform strain assumption. Gaussian probability density functions are observed for the relative displacements. No equipartition of energy is found.