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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 viscousplastic fluid. We choose a model of Bingham typetaking into account inhomogeneous yield limit of thefluid, which is well-adapted in the description oflandslides. After setting the generalthreedimensional problem, the blocking property isintroduced. We then focus on necessary andsufficient conditions such that blocking of the fluidoccurs.The anti-plane flow intwodimensional andonedimensional cases is considered.A variational formulation in terms of stresses isdeduced. More fine properties dealing with localstagnant regions as well as local regions where thefluid behaves like a rigid body are obtained indimension one.

Keywords

Viscoplastic fluidinhomogeneous Bingham modellandslidesblockingpropertynondifferentiable variationalinequalitieslocal 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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