Predicting Effective Coefficients of Perforated Conductive Media: A Hybrid Asymptotic Homogenization and Machine Learning Approach
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This study presents a framework for predicting the effective conductive properties of isotropic media containing a periodic array of circular holes, where the unit cell comprises multiple inclusions (polydispersity). We develop semi-analytical solutions by applying two asymptotic homogenization techniques: (i) a classical approach for a single poly-disperse unit cell, and (ii) a reiterated scheme for hierarchical structures. The associated boundary value problems are efficiently solved using the theory of functions of a complex variable. The derived formulas for the effective coefficients are validated against established theoretical models and available experimental data. Furthermore, we employ these formulas to generate comprehensive datasets, which are used to train machine learning models for the prediction of effective properties. The proposed methodology, validated for conductive media, is broadly applicable to the analysis of perforated structures with more general physical properties (e.g., elastic, thermal).
