Nonsmooth simulation of dense granular flows with pressure-dependent yield stress

Understanding the flow of granular materials is of utmost importance for numerous industrial applications including the manufacturing, storing and transportation of grain assemblies (such as cement, pills, or corn), as well as for natural risk assessing considerations. Discrete Element Modeling (DEM) methods, which explicitly represent grain-grain interactions, allow for highly-tunable and precise simulations, but they suffer from a prohibitive computational cost when attempting to reproduce large scale scenarios. Continuum models have been recently investigated to overcome such scalability issues, but their numerical simulation still poses many challenges. In this work we propose a novel numerical framework for the continuous simulation of dilatable materials with pressure-dependent (Coulomb) yield stress. Relying upon convex optimization tools, we show that such a macroscopic, nonsmooth rheology can be interpreted as the exact analogous of the solid frictional contact problem at the heart of DEM methods, extended to the tensorial space. Combined with a carefully chosen finite-element discretization, this new framework allows us to avoid regularizing the continuum rheology while benefiting from the efficiency of nonsmooth optimization solvers, mainly leveraged by DEM methods so far. Our numerical results successfully compare to analytic solutions on model problems, and we retrieve qualitative flow features commonly observed in reported experiments of the literature.