A non-local constitutive model for slow granular flow that incorporates dilatancy

Over the past two decades several attempts have been made to formulate constitutive models for slow granular flow to remedy the deficiencies of classical plasticity. All the proposed models assume the medium to be incompressible, though it is well known that density change accompanies deformation in...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 888
Main Authors Dsouza, Peter Varun, Nott, Prabhu R.
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 10.04.2020
Subjects
Computational fluid dynamics
Computer simulation
Constitutive models
Deformation
Deformation mechanisms
Density
Dilatancy
Granular materials
Gravity
Mathematical models
Model testing
Shear deformation
Shear flow
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Summary:Over the past two decades several attempts have been made to formulate constitutive models for slow granular flow to remedy the deficiencies of classical plasticity. All the proposed models assume the medium to be incompressible, though it is well known that density change accompanies deformation in granular materials. A particularly important aspect of density change that is distinctive of granular materials is dilatancy, or volume deformation caused by shear deformation. No constitutive model for sustained flow has thus far captured dilatancy. Here we present a non-local constitutive model wherein the deformation rate and density at a point depend on the state of stress in a mesoscopic region around it. Apart from incorporating dilatancy, our model has a physical origin that is distinct from that of the previously proposed non-local models. We test our model on simple shear flow in the absence and presence of gravity, and find its predictions to be in good agreement with particle dynamics simulations.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2020.62