Continuum Modeling and Computational Aspects of Flowing Granular Media

Department of Mechanical Engineering 

Massachusetts Institute of Technology

Bulk granular materials have surprisingly complicated mechanical properties.  Moreover, their ability to both flow like a fluid and behave as a stiff solid makes continuum simulation challenging computationally.  As a result, basic problems such as predicting the flow profile in a draining hourglass have proven to be a significant challenge.  We begin by developing a constitutive law that can be used to predict the stress and velocity profiles in well-developed granular flows.  This is achieved by merging recent models for granular elasticity and rate-sensitive plastic flow into one universal elasto-plastic law, capable of determining flowing regions and stagnant zones simultaneously in any arbitrary 3D flow geometry.  The model is numerically implemented using FEM and results are directly compared to experiments and discrete particle simulations in several inhomogeneous flow geometries.  The computational issues that arise in simulating this type of "solid flow" point to the potential advantages of an Eulerian-based computational scheme amenable to fixed-space boundary conditions and well-developed flow.  On this front, we introduce a technique for solid simulation on a fixed grid, with potential to simplify the simulation of highly deformable solid materials.  As shall be demonstrated, the approach extends naturally to the simulation of unrelated problems such as fluid/structure interaction, large-strain elasticity, and various other plasticity models.