Transient stress and fabric model for quasi-static granular flows in three dimensions

We present and validate a general three-dimensional continuum model for predicting the coupled fabric and stress transient response in 3D dense granular flows for the quasi-static regime. The model is inspired by isotropic and kinematic hardening theory, which is widely applied to plastic loading cycles in metals, which constitutes a connection between two different flowing materials through the same plastic modeling framework. The first part of the model consists of a differential evolution equation for the fabric tensor, which incorporates a new parameter called contact persistence to model the capacity of the fabric network to keep its contacts according to the relative direction of the shear-rate. The second part of the model is an expression for the shear stress comprised of a backstress, proportional to the fabric tensor, and a term proportional to the shear-rate direction. This shear stress decomposition was obtained from DEM data extracted within a 3D Couette cell during unsteady processes wherein the shear-rate direction rotates instantaneously with respect to the axis perpendicular to the walls of the cell. The results of the model are compared with DEM simulations for different changes in shear orientation, achieving a good agreement for the evolution of the fabric and deviatoric stress tensors. The model is shown to be compatible with the second law of thermodynamics, revealing that the origin of the backstress flow resistance in granular media is distinct from the cause of backstresses in metals; rather than arising from stored defect energy, it arises from the dependence of dilatancy on the alignment of the fabric and flow-rate.