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

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