Granular materials are very common, comprising geophysical matter (sand, gravel, soils), industrial raw materials, food stuffs, and pharmaceuticals to name a few.  Granular media is second only to water as the most handled material in global industry.  However, unlike standard fluids or elastic solids, these materials lack a well-understood theoretical foundation; there is no universal continuum model to predict the behavior of granular media in an arbitrary geometry under arbitrary loading. Particle-by-particle discrete simulations can be used, but these become computationally intractable for large systems and large times. Indeed, it is an open and pressing challenge to determine a predictive granular continuum model, which can correctly represent many millions of particles interacting through dissipative, frictional contacts.

Because granular media can switch its behavior from solid-like (able to support static shear loads), to liquid-like (it can flow in a dense state), to gas-like (grains can separate and collide), progress on granular modeling requires a combination of tools from solid mechanics, fluid mechanics, and statistical physics. Our work in the Kamrin Group embraces the multidisciplinary nature of this problem and employs methods from all of these fields in an attempt to find fundamental physical relations that govern granular media. We have built a heirarchy of continuum models for flowing grains that capture many of the strange behaviors of these materials and can predict granular motion with a high level of accuracy. Oftentimes, we utilize discrete-particle simulations as a "computer experiment" to help elucidate meso-scale principles and verify relations in our models. We have also developed acoustic models of realistic dense-packed granular systems, and we are currently building models for wet granular media and electrically conductive particulate media.

One thrust in our group is the development of a nonlocal continuum approach for granular media. Nonlocality emerges due to the cooperativity of grain motion, which is scaled inherently by the size of the grains themselves. This causes the mechanical properties at some location to be influenced by the flow taking place at all other locations. The effect is non-trivial and plays a significant role in the development of granular flow fields, but it has been historically difficult to model. To address this issue we proposed the "Nonlocal Granular Fluidity" model, which builds a size-effect directly into the response. Its success is marked by the ability to quantitatively predict flows in many different 2D geometries and over a hundred 3D experiments, each without parameter adjustment. This level of generality and precision is unprescendented in granular flow theory, especially for a model in which only one new material parameter is introduced. There are a number of other manifestations of finite-size effects that have been observed in granular materials and it appears the nonlocal model explains these equally well, including the fact that thin zones of grains behave as if they are stronger and the "secondary rheology" phenomenon wherein far-away motion effectively erases the yield criterion everywhere. To illustrate the physical consistency of the model we have carried out an in-depth thermomechanical analysis of the system, and have performed a parameter study to understand the basis of our new material parameter, the nonlocal amplitude.

We have also developed a simplified continuum model called the "trans-phase frictional plastic model" that has proven useful for modeling off-road traction applications. This model allows material to transit between the dense (solid-like and liquid-like) and separated (gas-like) regimes, a frequent occurence in problems involving objects intruding through granular beds. The model is currently being used to simulate the VIPER rover, which is set to go to the moon in 2024, as part of a large NASA collaboration. The model also indicates the presence of a set of Granular Scaling Laws (GSL) which can be used to predict the performace of vehicles under non-earth gravity using only earthbound tests.

Experiments have indicated that a very simple surface resistance model (called granular RFT) works well to predict resistive forces on arbitrarily-shaped solids being dragged through grains. We have found the first mechanical explanation of this surprising reduction in complexity, relating the effect to an invariance within the trans-phase model. With explanation in hand, the mechanical picture further details why viscous fluids do not have as strong  a collapse to simple resistance models. It also allows us to predict new materials that ought to have one. We recently showed the ability to use this approach beyond slow movements, to accurately model rapid intrusion phenomena like running and driving on loose terrains.  Here, the material agitation from the locomotor makes the material beahvior appear to switch between solid, liquid, and gas perpetually.  We have shown that despite gthis complexity, the same basic continuum model reproduces the forces of the terrain on the moving locomotor. Further, by analysing the model results, we discovered a new surface-resistance model that can be used to describe the behavior of fast locmotors, which we have called Dynamic RFT.     

External collaborators:

David Henann (Brown)
Georg Koval (INSA Strasbourg)
Dan Goldman (Georgia Tech)               

Media:

MIT News articles and videos (click here, here, here, here, or here) describing challenges in granular flow and our recent modeling developments. Feature article in Physics Today.

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