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The blocking of an inhomogeneous Bingham fluid.Applications to landslides

Published online by Cambridge University Press:  15 January 2003

Patrick Hild ,
Ioan R. Ionescu ,
Thomas Lachand-Robert  and
Ioan Roşca
Patrick Hild
Affiliation:
Laboratoire de Mathématiques, UMR CNRS 5127, Université de Savoie, 73376 Le Bourget-du-Lac Cedex, France. thomas.lachand-robert@univ-savoie.fr., ionescu@univ-savoie.fr. Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France. Patrick.Hild@descartes.univ-fcomte.fr.
Ioan R. Ionescu
Affiliation:
Laboratoire de Mathématiques, UMR CNRS 5127, Université de Savoie, 73376 Le Bourget-du-Lac Cedex, France. thomas.lachand-robert@univ-savoie.fr., ionescu@univ-savoie.fr.
Thomas Lachand-Robert
Affiliation:
Laboratoire de Mathématiques, UMR CNRS 5127, Université de Savoie, 73376 Le Bourget-du-Lac Cedex, France. thomas.lachand-robert@univ-savoie.fr., ionescu@univ-savoie.fr.
Ioan Roşca
Affiliation:
Department of Mathematics, University of Bucharest, Str. Academiei, 14, 70109 Bucharest, Romania. rosca@math.math.unibuc.ro.
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Abstract

This work is concerned with the flow of a viscous plastic fluid. We choose a model of Bingham type taking into account inhomogeneous yield limit of the fluid, which is well-adapted in the description of landslides. After setting the general threedimensional problem, the blocking property is introduced. We then focus on necessary and sufficient conditions such that blocking of the fluid occurs. The anti-plane flow in twodimensional and onedimensional cases is considered. A variational formulation in terms of stresses is deduced. More fine properties dealing with local stagnant regions as well as local regions where the fluid behaves like a rigid body are obtained in dimension one.

Keywords

Viscoplastic fluidinhomogeneous Bingham modellandslidesblocking propertynondifferentiable variational inequalitieslocal qualitative properties.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 6 , November 2002 , pp. 1013 - 1026
Copyright
© EDP Sciences, SMAI, 2002

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