Exact Expansion Formalism for Transport Properties of Heterogeneous Materials Characterized by Arbitrary Continuous Random Fields

2025/05/22 by Liyu Zhong, Zhong, Liyu, Sheng Mao +1
Materials Science · Engineering · Mathematics · #Thermal properties of materials #Composite Material Mechanics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2505.16173

Abstract

We derive an exact contrast-expansion formalism for the effective conductivity of heterogeneous materials (media) with local properties described by arbitrary continuous random fields, significantly generalizing the widely used binary-field models. The theory produces a rapidly convergent Neumann-series that, upon Gaussian closure via a Hermite expansion, yields closed-form first-, second- and third-order approximations, which achieve percent-level accuracy at first order for isotropic media. For anisotropic media, second-order approximations achieve sub-2% accuracy across a wide range of local property contrasts and correlations. Our formalism provides mathematically rigorous structure-property closures, with significant implications for the discovery and design of novel graded and architected materials with tailored transport properties.

Citations

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