Well-posed continuum equations for granular flow with compressibility and μ ( I )-rheology

Barker, T., Schaeffer, D. G., Shearer, M. and Gray, J. M. N. T. 2017. Well-posed continuum equations for granular flow with compressibility and μ ( I )-rheology. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2201) , 20160846. 10.1098/rspa.2016.0846

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Abstract

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Publisher:	The Royal Society
ISSN:	1364-5021
Date of First Compliant Deposit:	22 September 2021
Date of Acceptance:	4 April 2017
Last Modified:	18 May 2023 13:56
URI:	https://orca.cardiff.ac.uk/id/eprint/144013

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