Tuesday, 12 October 2004 - 3:30 PM

This presentation is part of : Rajagopal Symposium

Configurational Thermomechanics of Diffusive Systems

Gerard A. Maugin, Universite Pierre et Marie Curie, Laboratoire de Modelisation en Mecanique, Universite Pierre et Marie Curie, Laboratoire de Modelisation en Mecanique, Case 162, 4 place Jussieu, 75252 Paris, Cedex 05, 75252, France

Configurational or " material " mechanics of continua is the mechanics of changes and evolution of material configurations. It is thus well adapted to the formulation of a theory of material growth as also to the numerics of the evolution of material patterns, especially in the presence of material defects. Accordingly, it probably offers the best framework for formulating many problems related to the evolution of biological tissues. However, growth of such tissues cannot be studied without invoking the influence of nutriments or, in other words, input of energy in some way or another. The present contribution explores the basics of the configurational mechanics of thermoelastic media in the presence of diffusive effects. The latter are shown to influence the formulation of the balance of material momentum (the relevant equation for further consideration of structural defects) in two different ways, by modifying the expression of the Eshelby stress tensor - that provides the driving force behind the evolution of material configurations -, and adding source terms in that equation. Completing the scheme with electric effects - which may be relevant - follows the same line of thought.

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