Anisotropic inertia rheology of ellipsoidal grains

Abstract

Ellipsoidal grains show a complex macroscopic response associated with their microscopic ability to orient and align with respect to each other and the ambient flow. These additional microscopic degree of freedom is an evolving property that gives rise to a complex anisotropic macroscopic mechanical response. Available models for dense granular flow typically only consider grain size while ignoring grain shape, orientation and alignment and their effect on the macroscopic mechanical response. This paper discusses the construction of a generalized inertia rheology model for ellipsoidal grains. The construction of the continuum model incorporates the microstructure that accounts for the grains’ orientation and alignment and utilizes the representation theorem and dissipation inequality to yield a simple and physically meaningful phenomenological model. The model predictions show good agreement compared to available Discrete Element Method simulations of simple shear flow. The proposed model is complete in the sense that it consists of a constitutive law that relates the microstructure arrangement and the flow to the developed stresses supported by an evolution law for the microstructure arrangement.