The blocking of an inhomogeneous Bingham fluid. Applications to landslides
Laboratoire de Mathématiques, UMR CNRS 5127,
Université de Savoie, 73376 Le Bourget-du-Lac Cedex, France. firstname.lastname@example.org., email@example.com.
2 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.
3 Department of Mathematics, University of Bucharest, Str. Academiei, 14, 70109 Bucharest, Romania. firstname.lastname@example.org.
Revised: 3 May 2002
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.
Mathematics Subject Classification: 49J40 / 76A05
Key words: Viscoplastic fluid / inhomogeneous Bingham model / landslides / blocking property / nondifferentiable variational inequalities / local qualitative properties.
© EDP Sciences, SMAI, 2002