Abstract
Granular materials have a strange propensity to behave as either a complex media or a simple media depending on the precise question being asked. This review paper offers a summary of granular flow rheologies for well-developed or steady-state motion, and seeks to explain this dichotomy through the vast range of complexity intrinsic to these models. A key observation is that to achieve accuracy in predicting flow fields in general geometries, one requires a model that accounts for a number of subtleties, most notably a nonlocal effect to account for cooperativity in the flow as induced by the finite size of grains. On the other hand, forces and tractions that develop on macro-scale, submerged boundaries appear to be minimally affected by grain size and, barring very rapid motions, are well represented by simple rate-independent frictional plasticity models. A major simplification observed in experiments of granular intrusion, which we refer to as the ‘resistive force hypothesis’ of granular Resistive Force Theory, can be shown to arise directly from rate-independent plasticity. Because such plasticity models have so few parameters, and the major rheological parameter is a dimensionless internal friction coefficient, some of these simplifications can be seen as consequences of scaling.
Highlights
Granular materials have a well-deserved reputation as a complex rheological media [1]
We summarize three granular flow models, each adding more complexity to the one before it
Granular flow models have a wide assortment of complexity
Summary
Granular materials have a well-deserved reputation as a complex rheological media [1]. Dry granular systems display history- and preparation-dependent strengthening and dilation [2,3,4], flow anisotropy and normal stress differences [5,6,7], nonlinear rate-sensitive yielding [8,9,10,11], and nonlocality due to the finite size of grains [12,13,14,15,16] All these phenomena depend sensitively on grain characteristics such as shape and size distribution, frictional properties, and stiffness [10, 17,18,19,20]. We begin by describing the continuum models at hand, and follow up with demonstrations focusing on weighing the need for simpler models, which are more amenable to analytical tools, with the need for more detailed forms that have greater field accuracy but at a larger computational cost
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