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Specific features of the homogenization problems for matrix composite materials and polycrystals are considered. Relations between the ensemble and spatial averages of the fields in heterogeneous media are discussed. The representative volume element of the medium is introduced. Integral equations for the fields in heterogeneous media are derived. Cross-property relations between effective characteristics of different physical natures are indicated.

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The Homogenization Problem

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  • 发表日期：

    2025年

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  • Sergey Kanaun

摘要

Specific features of the homogenization problems for matrix composite materials and polycrystals are considered. Relations between the ensemble and spatial averages of the fields in heterogeneous media are discussed. The representative volume element of the medium is introduced. Integral equations for the fields in heterogeneous media are derived. Cross-property relations between effective characteristics of different physical natures are indicated.