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.