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Modélisation des milieux à microstructure : approches par la méthode des puissances virtuelles

Abstract : The first part (chapt. 1) of this Ph.D. thesis is dedicated to a bibliographic analysis. A rapid survey of the main works on the topic of continua with microstructure is used as an introduction to the simple materials theory of W. Noll and to a short exposition of the works of G. Capriz. The next step (chapt. 2) consists in the explanation of the "deep" space notion and of the relevant microplacement and macroplacement of a set of particles in that deep space. The properties of these placements determine the definitions of each continuum : monoparticular, multiparticular, multiconstituents or multiphasic. We give the cinematic and dynamic properties of those continua, and propose the possibility for the use of a phase functions field to deal with the evolution of the phases. Two different ways (chapt.3) are proposed to write the field and boundary equations of a multiparticular continuum with microstructure. The aim is to describe the equilibrium state of a Cosserat multiparticular continuum - i. e. a continuum in each point of which a continuum of triads is to be considered. Chapter four is the exposition of a new micro-macro transformation method which we named "globalization." This one is derived from the classical homogenization methods. It consists in defocusing a classical continua with microstructure (monoparticular), in order to obtain either the equilibrium equations or the constitutive variables of the macro continua from those of the initial medium. The method is developed for the case of microstructures represented in a manifold on which the action of the group of the rotations of the three dimensional Euclidean space is transitive. The end of the report (chapt. 5) deals with a few proposals to try to determine the behavior - in relation with the behavior of the micro-continuum. - of such multiparticular continua with microstructure.
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Philippe Tamagny. Modélisation des milieux à microstructure : approches par la méthode des puissances virtuelles. Mécanique []. Ecole Nationale des Ponts et Chaussées, 1996. Français. ⟨tel-00523015⟩



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