DOI: 10.1051/jp2:1991167
J. Phys. II France 1 (1991) 265-272

Current-conductance and stress-elastic modulus correlations

Stéphane Roux¹, François Hild², Didier Fokwa², Denis Breysse², Giusepe Geymonat² and Gilles Pijaudier-Cabot<sup>2

1</sup>  Centre d'Enseignement et de Recherche en Analyse des Matériaux, Ecole Nationale des Ponts et Chaussées, 1 Avenue Montaigne, Central IV, F-93167 Noisy le Grand Cedex, France
²  Laboratoire de Mécanique et Technologie, Ecole Normale Supérieur de Cachan, Université Paris VI, 61 Avenue du Président Wilson, F-94235 Cachan Cedex, France

(Received 5 December 1990, accepted 17 January 1991)

Abstract
We consider a composite medium which consists in resistance elements with a distibution of conductance, in a narrow range around a mean value. The question we address is the distibution of local power dissipation, and its correlation with the local conductance. Various discretizations of the problem are considered: regular networks of different types in two and three dimensions whose bonds are assigned conductances at random, finite element method with random distibution of conductances in each element. We also consider the case of elastic elements, and study the distibution of elastic energy stored in each element. It is shown that the correlation between the dissipated (or elastic) energy and the conductance (or elastic modulus) depends on the discretization. These correlations are analysed in an effective medium theory framework, and numerical simulations confirm the theoretical predictions. The distribution of local energy always tends towards a Gaussian distibution for all cases considered, in the limit of a small disorder.

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