Current-conductance and stress-elastic modulus correlations

Stéphane G. Roux , François Hild , Didier Fokwa , Denis Breysse , Giusepe Geymonat , Gilles Pijaudier-Cabot

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.

Domaines: Articles anciens

Stéphane G. Roux, François Hild, Didier Fokwa, Denis Breysse, Giusepe Geymonat, et al.. Current-conductance and stress-elastic modulus correlations. Journal de Physique II, 1991, 1 (3), pp.265-272. ⟨10.1051/jp2:1991167⟩. ⟨jpa-00247515⟩