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Formulation thermodynamique de lois de comportement hors-équilibre

Abstract : Strategies for the elaboration of Lagrangian formulations of the constitutive laws of continuous media subjected to local dissipation are developed. The computation of the resulting variational and local continuous symmetries constitutes the backbone of this work. The theoretical framework chosen is based on a thermodynamics of relaxations, which allows the consideration of microstructural variables evolution, accounting for the kinetic law describing the evolution of the microstructure. It is demonstrated that the self-adjointness condition, which is the necessary and sufficient condition for the existence of a lagrangian associated to a system of partial differential equations, is fulfilled by the chosen constitutive laws, provided the fundamental Euler relation is being generalized for situations outside equilibrium. This postulate is one of the cornerstone of a thermodynamics of relaxation called DNLR (alias Distribution of Nonlinear Relaxations). The kinetics equations governing the evolution of the microstructural variables has been further incorporated into the Lagrangian by means of mul- tipliers. The second aspect exploted in this work concerns the analysis of the Lie symmetries of the constitutive behaviour, following two different routes, The first one consists in computing the variational symmetries, associated to given constitutive equations. A particular symmetry is highlighted in the case of a simplified DNLR model, that is related to the time-temperature equivalence principle. Enlarging the point of view, a methodology for setting up the constitutive behaviour of the material itself is proposed. It relies on the construction of experimental master curves that are given a Lie group structure, further leading to a formal structure of the constitutive equations. This method has been applied for a stick submitted to an impact loading under large strain.
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Vincent Magnenet. Formulation thermodynamique de lois de comportement hors-équilibre. Autre [cond-mat.other]. Institut National Polytechnique de Lorraine, 2004. Français. ⟨NNT : 2004INPL107N⟩. ⟨tel-01749694⟩



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