LOCAL RHEOLOGY OF DENSE GRANULAR FLOWS WITH MIXED GRANULAR TEMPERATURE GENERATION

Abstract

This thesis investigates proposed constitutive laws for dense granular flows using particle-based simulations of planar shear under varying stress conditions. Granular materials are prevalent in both science and industry, yet a fully local relationship between stress and strain rate remains elusive. A widely used model links the stress ratio to a dimensionless shear rate, but it breaks down in slow-flowing regimes, predicting no motion where deformation persists. Nonlocal models incorporating a diffusive fluidity parameter can resolve this issue in certain geometries. Alternatively, local models grounded in kinetic theory that incorporate granular temperature—a measure of grain velocity fluctuations—also show promise.To evaluate these models, we simulate flows with stress gradients induced by gravity and mechanical vibration, producing granular temperature under mixed driving conditions. Our findings yield four primary conclusions. First, the fluidity-based model does not collapse well, particularly under mechanical vibration. Second, a granular temperature-based model more accurately reproduces flow behavior in both vibrated and mixed cases. Third, packing fraction, though often treated as fundamental, is not a controlling variable in these formulations. Finally, observed stress and temperature anisotropies suggest that modeling granular temperature through kinetic theory may be more complex than previously anticipated.