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.
Mots-clés : viscoplastic fluid, inhomogeneous Bingham model, landslides, blocking property, nondifferentiable variational inequalities, local qualitative properties
@article{M2AN_2002__36_6_1013_0,
author = {Hild, Patrick and Ionescu, Ioan R. and Lachand-Robert, Thomas and Ro\c{s}ca, Ioan},
title = {The blocking of an inhomogeneous {Bingham} fluid. {Applications} to landslides},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1013--1026},
publisher = {EDP-Sciences},
volume = {36},
number = {6},
year = {2002},
doi = {10.1051/m2an:2003003},
mrnumber = {1958656},
zbl = {1057.76004},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2003003/}
}
TY - JOUR AU - Hild, Patrick AU - Ionescu, Ioan R. AU - Lachand-Robert, Thomas AU - Roşca, Ioan TI - The blocking of an inhomogeneous Bingham fluid. Applications to landslides JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2002 SP - 1013 EP - 1026 VL - 36 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003003/ DO - 10.1051/m2an:2003003 LA - en ID - M2AN_2002__36_6_1013_0 ER -
%0 Journal Article %A Hild, Patrick %A Ionescu, Ioan R. %A Lachand-Robert, Thomas %A Roşca, Ioan %T The blocking of an inhomogeneous Bingham fluid. Applications to landslides %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 1013-1026 %V 36 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003003/ %R 10.1051/m2an:2003003 %G en %F M2AN_2002__36_6_1013_0
Hild, Patrick; Ionescu, Ioan R.; Lachand-Robert, Thomas; Roşca, Ioan. The blocking of an inhomogeneous Bingham fluid. Applications to landslides. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 6, pp. 1013-1026. doi : 10.1051/m2an:2003003. http://archive.numdam.org/articles/10.1051/m2an:2003003/
[1] , Fluidity and plasticity. Mc Graw-Hill, New-York (1922).
[2] and, Constitutive model and analysis of creep flow of natural slopes. Ital. Geotech. J. 34 (2000) 44-54.
[3] , Plastical flow through conical converging dies, using viscoplastic constitutive equations. Int. J. Mech. Sci. 17 (1975) 425-433. | Zbl
[4] , On the optimal die angle in fast wire drawing. J. Mech. Work. Technol. 3 (1980) 275-287.
[5] , A model of stability of slopes in Slope Stability 2000. Proceedings of Sessions of Geo-Denver 2000, D.V. Griffiths, G.A. Fenton and T.R. Martin (Eds.). Geotechnical special publication 101 (2000) 86-98.
[6] , and, A model for slow motion of natural slopes. Can. Geotech. J. (to appear).
[7] and, Ordinary differential equations, Sobolev spaces and transport theory. Invent. Math. 98 (1989) 511-547. | Zbl
[8] and, Les inéquations en mécanique et en physique. Dunod, Paris (1972). | MR | Zbl
[9] , Lectures on numerical methods for nonlinear variational problems. Notes by M.G. Vijayasundaram and M. Adimurthi. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 65. Tata Institute of Fundamental Research, Bombay; Springer-Verlag, Berlin-New York (1980). | MR | Zbl
[10] , and, Analyse numérique des inéquations variationnelles. Tome 1 : Théorie générale et premières applications. Tome 2 : Applications aux phénomènes stationnaires et d'évolution. Méthodes Mathématiques de l'Informatique, 5. Dunod, Paris (1976). | Zbl
[11] and, The blocking property in the study of the Bingham fluid. Int. J. Engng. Sci. 24 (1986) 289-297. | Zbl
[12] and, Functional and numerical methods in viscoplasticity. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York (1993). | MR | Zbl
[13] and, A numerical method for a viscoplastic problem. An application to the wire drawing. Internat. J. Engrg. Sci. 26 (1988) 627-633. | Zbl
[14] and, Variational inequalities. Comm. Pure. Appl. Math. XX (1967) 493-519. | Zbl
[15] , Mathematical Topics in Fluid Mechanics, Vol 1: Incompressible models. Oxford University Press (1996). | MR | Zbl
[16] and, Variational methods in the theory of the fluidity of a viscous-plastic medium. PPM, J. Mech. and Appl. Math. 29 (1965) 545-577. | Zbl
[17] and, On stagnant flow regions of a viscous-plastic medium in pipes. PPM, J. Mech. and Appl. Math. 30 (1966) 841-854. | Zbl
[18] and, On qualitative singularities of the flow of a viscoplastic medium in pipes. PPM, J. Mech and Appl. Math. 31 (1967) 609-613. | Zbl
[19] and, An existence theorem for the multifluid Navier-Stokes problem. J. Differential Equations 122 (1995) 71-88. | Zbl
[20] , A rational formulation of the equations of plastic flow for a Bingham solid. Proc. Camb. Philos. Soc. 43 (1947) 100-105. | Zbl
[21] , Un espace fonctionnel pour les équations de la plasticité. Ann. Fac. Sci. Toulouse Math. (6) 1 (1979) 77-87. | Numdam | Zbl
[22] , Navier-Stokes Equations. Theory and Numerical Analysis. North-Holland, Amsterdam (1979). | MR | Zbl
[23] , Problèmes mathématiques en plasticité. Gauthiers-Villars, Paris (1983). | MR | Zbl
[24] and, Functions of bounded deformation. Arch. Rational Mech. Anal. 75 (1980) 7-21. | Zbl
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