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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2505.16173 |
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| _version_ | 1866908529417256960 |
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| author | Zhong, Liyu Mao, Sheng |
| author_facet | Zhong, Liyu Mao, Sheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Expansion Formalism for Transport Properties of Heterogeneous Materials Characterized by Arbitrary Continuous Random Fields Zhong, Liyu Mao, Sheng Materials Science 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. |
| title | Exact Expansion Formalism for Transport Properties of Heterogeneous Materials Characterized by Arbitrary Continuous Random Fields |
| topic | Materials Science |
| url | https://arxiv.org/abs/2505.16173 |