Computer modeling of the conductivity of composites with a chaotic structure

Abstract

A scheme is proposed for calculating the effective conductivity of a two-component composite with a chaotic structure, based on a model of a three-dimensional lattice (two-dimensional in the planar case) consisting of nodes connected by conducting and non-conducting bonds. The lattice is analyzed for the presence of a connecting set (CS) of conducting bonds. It is shown that the conductivity of a lattice containing a CS with a random distribution of bonds is equal to the conductivity of a lattice containing a CS with an ordered distribution of bonds (of the "rectangle in rectangle" type), multiplied by the probability that a conducting bond belongs to the CS.