Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Journal articles

The effective conductivity of strongly nonlinear media: The dilute limit

Abstract : This work is a combined numerical and analytical investigation of the effective conductivity of strongly nonlinear media in two dimensions. The nonlinear behavior is characterized by a threshold value for the maximal absolute current. Our main focus is on random media containing an infinitesimal proportion f≪1 of insulating phase. We first consider a random conducting network on a square grid and establish a relationship between the length of minimal paths spanning the network and the network's effective response. In the dilute limit f≪1, the network's effective conductivity scales, to leading-order correction in f, as ~f^ν with ν=1 or ν=1/2, depending on the direction of the applied field with respect to the grid. Second, we introduce coupling between local bonds, and observe an exponent ν≈2/3. To interpret this result, we derive an upper-bound for the length of geodesics spanning random media in the continuum, relevant to media with a dilute concentration of heterogeneities. We argue that ν=2/3 for random composites in the continuum with homogeneously-distributed, monodisperse particles, in two dimensions.
Document type :
Journal articles
Complete list of metadata
Contributor : François Willot Connect in order to contact the contributor
Submitted on : Friday, December 25, 2020 - 10:31:09 PM
Last modification on : Wednesday, November 17, 2021 - 12:28:40 PM


Files produced by the author(s)





François Willot. The effective conductivity of strongly nonlinear media: The dilute limit. International Journal of Solids and Structures, Elsevier, 2020, Special Issue on Physics and Mechanics of Random Structures: From Morphology to Material Properties, 184, pp.287-295. ⟨10.1016/j.ijsolstr.2019.06.006⟩. ⟨hal-02425307⟩



Record views


Files downloads