Nonlocal Constitutive Relation for Steady Granular Flow
Name
Kamrin-2012-Nonlocal Constitutive Relation for.pdf
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Author(s)
Kamrin, Kenneth N.
Koval, Georg
Date Issued
April 2012
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Kamrin, Ken, and Georg Koval. “Nonlocal Constitutive Relation for Steady Granular Flow.” Physical Review Letters 108.17 (2012). © 2012 American Physical Society
Version
Final published version
Abstract
Extending recent modeling efforts for emulsions, we propose a nonlocal fluidity relation for flowing granular materials, capturing several known finite-size effects observed in steady flow. We express the local Bagnold-type granular flow law in terms of a fluidity ratio and then extend it with a particular Laplacian term that is scaled by the grain size. The resulting model is calibrated against a sequence of existing discrete element method data sets for two-dimensional annular shear, where it is shown that the model correctly describes the divergence from a local rheology due to the grain size as well as the rate-independence phenomenon commonly observed in slowly flowing zones. The same law is then applied in two additional inhomogeneous flow geometries, and the predicted velocity profiles are compared against corresponding discrete element method simulations utilizing the same grain composition as before, yielding favorable agreement in each case.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.108.178301
