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Mécanique des milieux poreux en transformation finie : formulation des problèmes et méthodes de résolution

Abstract : Some problems of practical interest in civil engineering as well as in petroleum engineering involve porous media whose skeleton undergo finite strains and finite rotations. As well as for monophasic continua, a formalism more complex than that used in the familiar framework of small perturbations is needed to take into account large changes of geometry. From a theoretical point of view, the main difficulty lies in the formulation of the behaviour: the approach proposed here consists in taking advantage of the study of the thermodynamics of the porous medium. Chapter 1 is devoted to the mechanical modelling of porous media developed by Biot, and to the framework designed by Coussy to study the thermodynamics of open continua. The formulation of the constitutive equations of an elastic porous medium is discussed in chapter 2. Special attention is paid to the case of materials whose skeleton is made of an incompressible solid. Chapter 3 compares the results obtained at finite strains with the results provided by a formulation built in the framework of infinitesimal strains, for the problems of the consolidation of a porous layer and of the compaction of sediments in poroelasticity. Chapter 4 deals with the behaviour of poroelastoplastic materials at large strains. We notably propose a model that generalizes the Cam-Clay model to porous media at large strains. Chapter 5 presents the principles of numerical solution of the equations of finite poroelastoplasticity, and the solution of a simple academic problem. It is pointed out that, for the problems discussed here, taking into account finite strains and rotations leads to results significantly different from those obtained in infinitesimal transformation, without giving rise to greater mathematical difficulties in the determination of the solution.
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Submitted on : Monday, October 25, 2010 - 3:25:44 PM
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Emmanuel Bourgeois. Mécanique des milieux poreux en transformation finie : formulation des problèmes et méthodes de résolution. Mécanique []. Ecole Nationale des Ponts et Chaussées, 1997. Français. ⟨tel-00529407⟩



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