Kinematic and static hypotheses for constitutive modelling of granulates considering particle rotation

The granular material perceived as a collection of particles is modelled as a Cosserat or multipolar continuum taking into account the effect of material microstructure. The macro-scale constitutive law for a granular material is derived from the micro-scale of two interacting particles. We adopt an approach based on a static hypothesis and establish two relationships: i) macro-to-micro static relationship, and ii) micro-to-macro kinematic relationship. We derive macro-scale constitutive constants for granular materials with idealized isotropic packing structure. The effects of inter-particle stiffness on the macro-scale constitutive constants are discussed. In addition, Green's function for concentrated force and couple is derived to be expressed in terms of inter-particle stiffness. Using the expressions of Green's function, the physical meaning and the effect of the internal characteristic length for granular materials are discussed.