Computer simulation results for bounds on the effective conductivity of composite media

This paper studies the determination of third‐ and fourth‐order bounds on the effective conductivity σe of a composite material composed of aligned, infinitely long, identical, partially penetrable, circular cylinders of conductivity σ2 randomly distributed throughout a matrix of conductivity σ1. Both bounds involve the microstructural parameter ζ2 which is a multifold integral that depends upon S3, the three‐point probability function of the composite. This key integral ζ2 is computed (for the possible range of cylinder volume fraction φ2) using a Monte Carlo simulation technique for the penetrable‐concentric‐shell model in which cylinders are distributed with an arbitrary degree of impenetrability λ, 0≤λ≤1. Results for the limiting cases λ=0 (‘‘fully penetrable’’ or randomly centered cylinders) and λ=1 (‘‘totally impenetrable’’ cylinders) compare very favorably with theoretical predictions made by Torquato and Beasley [Int. J. Eng. Sci. 24, 415 (1986)] and by Torquato and Lado [Proc. R. Soc. London Ser....

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