Connecting discrete particle mechanics to continuum granular micromechanics: Anisotropic continuum properties under compaction.

A systematic and mechanistic connection between granular materials' macroscopic and grain level behaviors is developed for monodisperse systems of spherical elastic particles under die compaction. The Granular Micromechanics Approach (GMA) with static assumption is used to derive the stiffness tensor of transversely isotropic materials, from the average behavior of particle-particle interactions in all different directions at the microscale. Two particle-scale directional density distribution functions, namely the directional distribution of a combined mechano-geometrical property and the directional distribution of a purely geometrical property, are proposed and parametrized by five independent parameters. Five independent components of the symmetrized tangent stiffness tensor are also determined from discrete particle mechanics (PMA) calculations of nine perturbations around points of the loading path. Finally, optimal values for these five GMA parameters were obtained by minimizing the error between PMA calculations and GMA closed-form predictions of stiffness tensor during the compaction process. The results show that GMA with static assumption is effective at capturing the anisotropic evolution of microstructure during loading, even without describing contacts independently but rather accounting for them in an average sense.