Toward General Rheological Models of Dry and Fluid-Saturated Granular Media

Dry and fluid-saturated granular media display multiple modeling challenges from a continuum perspective. Foremost is the search for quantitative and robust constitutive models, in order to robustly predict the flow and stress fields in a flowing body. However, a major challenge is also to find methods to implement these theories in non-trivial geometries up to huge deformations. Methods able to do this are needed not just to implement models in realistic settings of practical interest, but also to test the versatility and correctness of any proposed model, especially models that employ higher-order effects. In this talk we will discuss various continuum modeling approaches for dry and for fluid-saturated granular media. We will also present two numerical technqiues for running these models in general geometries. Key challenges on the modeling front include the importance (or lack thereof) of grain size, the various influences of an interstitial fluid phase, and modeling the granular ``phase transition’’ between solid-like, dense-flowing, and disconnected gas-like regions of material.