Frictional-collisional constitutive relations for granular materials, with application to plane shearing

P. C. Johnson, R. Jackson

Research output: Contribution to journalArticle

1290 Scopus citations

Abstract

Within a granular material stress is transmitted by forces exerted at points of mutual contact between particles. When the particles are close together and deformation of the assembly is slow, contacts are sustained for long times, and these forces consist of normal reactions and the associated tangential forces due to friction. When the particles are widely spaced and deformation is rapid, on the other hand, contacts are brief and may be regarded as collisions, during which momentum is transferred. While constitutive relations are available which model both these situations, in many cases the average contact times lie between the two extremes. The purpose of the present work is to propose constitutive relations and boundary conditions for this intermediate case and to solve the corresponding equations of motion for plane shear of a cohesionless granular material between infinite horizontal plates. It is shown that, in general, not all the material between the plates participates in shearing, and the solutions for the shearing material are coupled to a yield condition for the nonshearing material to give a complete solution of the problem.

Original languageEnglish (US)
Pages (from-to)67-93
Number of pages27
Journaljournal of fluid mechanics
Volume176
DOIs
StatePublished - Mar 1987
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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