Thermodynamics and phenomenology
Jean Lemaitre - Ahmed Benallal – René Billardon – Didier Marquis
Laboratoire de Mécanique et Technologie
Ecole Normale Supérieure de Cachan – CNRS – Université Paris 6
61, avenue du Président Wilson 94235 Cachan Cedex, France
Abstract: The general way to derive constitutive equations for different phenomena,
coupled or not, is briefly described with an emphasis on the choice of state variables
and analytical expressions for the state potential and the (pseudo) potential of
dissipation by qualitative experiments. Quantitative experiments are used to determine
the numerical values of the materials dependent parameters. Applications are given for
anisotropic damage coupled to stress-strain behaviour of materials, for aging coupled to
plasticity and for magneto-mechanical couplings. A brief on
localisation phenomena is given as a conclusion.
1. INTRODUCTION
1975! When just started, it was clear that experiments should play a
major role in the development of mechanics of materials, but how to bridge the gap
between esoteric theories and pragmatic measurements? Up to that time, the worlds of
theoreticians of thermodynamics and the world of experimentalists were completely
disconnected, both writing for their own world without almost any mutual
understanding. against
Fortunately we were the children of Paul Germain; he spent much time making basic
thermodynamics clear in order to teach it in an understandable way to graduate students
(Germain, 1973). It became clear that any material behaviour can be stated as a
mathematical model, provided the second principle of thermodynamics is fulfilled and
provided a proper choice of state variables, a proper choice of an analytical expression
of a state potential and a proper choice of another analytical expression of a
dissipative (pseudo-)potential F are made (Lemaitre and Chaboche, 1994). In this
sentence the word is used three times. This means that Thermodynamics gives
the framework for building models, but not all the keys. Fortunately, human sensibility
still plays a role:
The choice of variables depends upon the purpose of modelling: which
phenomena should be modelled, under which conditions, and which predictions should
209
G.A. Maugin et al. (eds.), Continuum Thermomechanics, 209-223.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.