  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.
