Material stability and localization in the nonlocal granular fluidity model for dense granular flow

A common and successful continuum model for steady, dense granular flows is the inertial rheology. Recent work has shown that under certain conditions, the inertial rheology displays a linear instability in which short wavelength perturbations grow at an unbounded rate - i.e., a Hadamard instability. This observation indicates that the inertial rheology is capable of describing strain localization; however, it also raises concerns regarding the robustness of numerical solutions. It has been shown that the inclusion of higher-order velocity gradients into the rheology can suppress the Hadamard instability, while not precluding the modeling of strain localization into diffuse shear bands. In this talk, we consider the nonlocal granular fluidity (NGF) model - which also involves higher-order flow gradients and has been shown to quantitatively describe a wide variety of steady, dense flows - and show that the NGF model successfully regularizes the Hadamard instability of the inertial rheology. We further apply the NGF model to the problem of strain localization in quasi-static plane-strain compression using nonlinear finite-element simulations in order to demonstrate that the model is capable of describing diffuse strain localization in a mesh-independent manner.