Predicting Granular Flows: Amorphous Continuum Modeling with a Length-Scale

The lack of a predictive, general model for dense granular flow is an obstacle in engineering applications and an expensive problem in industry. For well-developed flows, certain rheological approaches have been put forward, however these break down in regions of less rapid motion, where a markedly different behavior is observed that has resisted theoretical treatment for years. To produce a general granular flow model that combines the fast and slow regimes, together with appropriate plasticity relations for transient effects, would constitute a major step forward in the field and a lucrative tool in engineering design and geophysics. Inspired by recent successes in the study of emulsion flow, this project will investigate a nonlocal constitutive approach, whose direct inclusion of a particle length-scale may provide the missing piece.

With sophisticated and customized finite-element tools, preliminary tests indicate that this strategy leads to quantitatively accurate well-developed flow predictions in multiple flow geometries, including one family of geometries whose flow fields have never previously been described by a continuum model. Certain additional tests will be performed to clarify potential limitations of the model. To move beyond well-developed behavior and broaden the model, research will be conducted to merge the technique within a critical-state framework to capture transient dilation/strengthening/softening effects. Another aim is to build an improved theory for the nonlocal mechanism, and in so doing improve the interpretation of boundary conditions and thin-body effects. Once dry flows are understood in this way, enhanced finite-element tools shall be taken advantage of yet again to model fluid-saturated grains. The similar foundations of this model and related approaches used for emulsions draw important connections between granular matter and other amorphous materials. The flow-induces-flow mechanism and its ability to reproduce flow and stress fields so accurately suggests a microscopic picture that could solve many open questions in particulate flow problems. The theoretical investigation will help clarify this basic mechanism to improve generalization to other matter. The finite-element tools developed to implement the nonlocal granular flow model also open the door to modeling multiple coupled effects in particulate systems -- fluid permeability as mentioned, but conceivably a combination of other effects like electric-field interactions, diffusing species effects, and heat conduction.

Owing to the many fundamental applications of granular flow in industry, science, and engineering, the approach we propose together with its demonstrated accuracy will provide a key tool for predicting flows in general circumstances. The work to be carried out also involves a significant and integrated educational component. The PI has conducted several innovations in online education at MIT and proposes a number of ways to improve residential and public education using online tools. Presentations will also be made in the MIT Minority Introduction to Science and Engineering program, a six-week summer program encouraging talented minority students to pursue degrees in technical fields. Moreover, the PI will involve undergraduates in the research process and integrate research problems into his teaching. Broader impact within the scientific community will be made through continued organization of the New England Workshop on the Mechanics of Materials and Structures, and the APS mini-symposium Continuum Descriptions of Discrete Materials.