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arXiv · 2505.16173

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

Liyu Zhong·Sheng Mao
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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.

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Liyu Zhong, Sheng Mao. 2025-05-22. Exact Expansion Formalism for Transport Properties of Heterogeneous Materials Characterized by Arbitrary Continuous Random Fields. https://arxiv.org/abs/2505.16173

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