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

Research output: Contribution to journalArticle

  • Authors:
  • Thomas Barker
  • D. G. Schaeffera
  • M. Shearer
  • JMNT GRAY

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

Bibliographical metadata

Original languageEnglish
JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Volume473
Issue number2201
Early online date3 May 2017
DOIs
StatePublished - 2017