Mathematical Issues in the Continuum Formulation of Slow Granular Flow
This lecture is a survey of certain mathematical problems arising in the description of the flow of granular materials such as sand, coal, or various raw materials used in industry. The rather long title is intended to convey what is not covered. We refer to slow flow in contrast to the rapid shearing flow considered by many authors (cf. the article by Jenkins in these Proceedings). In the case of rapid shearing it is possible to derive constitutive relations from first principles; the constitutive relations used here are purely phenomenological. We refer to a continuum formulation in contrast to particle simulations (cf. the article by Walton in these Proceedings). Although two phase flow was a major theme at the Workshop, we shall not consider the interaction of the granular medium with the interstitial fluid. We have retained the informal style of the lecture in this article.
KeywordsConstitutive Relation Granular Material Yield Surface Granular Medium Granular Flow
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- P.C. Johnson and R. Jackson, Frictional-collisional constitutive relations for granular materials, with applications to plane shearing, JFM 176 (1987), pp. 07–93.Google Scholar
- J. Mandel, Conditions de Stabilie et Postulat de Drucker, in Rheology and Soil Mechanics, Kraotchenko and P. Sirieys (eds.), IUTAM Symposium at Grenoble, April (1964), pp. 58–68.Google Scholar
- W. Praeger, Introduction to the Mechanics of Continua, Giun, Watham MA (1961).Google Scholar
- D. Schaeffer, Instability and ill-posedness in the deformation of granular materials, Int’L J. Num. Anal. Methods Geomech., (to appear).Google Scholar
- D. Schaeffer, M. Shearer, E.B. Pitman, Instability in critical state theories of granular How, SIAM J. Appl. Math, (to appear).Google Scholar