Elastic constants for granular materials modeled as first-order strain-gradient continua

Formulation of a stress–strain relationship is presented for a granular medium, which is modeled as a first-order strain-gradient continuum. The elastic constants used in the stress–strain relationship are derived as an explicit function of inter-particle stiffness, particle size, and packing density. It can be demonstrated that couple-stress continuum is a subclass of strain-gradient continua. The derived stress–strain relationship is simplified to obtain the expressions of elastic constants for a couple-stress continuum. The derived stress–strain relationship is compared with that of existing theories on strain- gradient models. The effects of inter-particle stiffness and particle size on material constants are discussed.