Application of AI and Machine Learning to the Theory of Composite Materials
V. V. Mityushev, K. B. Nurtazina, N. Z. Nauryzbayev
Quarterly No. 1, 2025 pages 11-20
DOI: https://doi.org/10.62753/ctp.2025.06.1.1
keywords: artificial intelligence, machine learning, composite material, multi-scale problem, microstructure, homogenization, structural sum
abstract The homogenization for classifying composites and determining their effective properties is an important optimal design problem of material sciences studied by mathematical modeling. The application of artificial intelligence (AI) and machine learning (ML) in the theory of composite materials is discussed. One of the main problems is the choice of characteristic ML features to describe multi-scale dispersed random composites and to predict their macroscopic properties. The complexity drastically increases when confronted with tasks such as estimating the effective properties of random composites, exploring optimal design scenarios with variable properties of components, or determining the optimal location and shape of inclusions since the myriad use of numerical computations proves challenging due to constraints in time and memory. In such instances, analytical, exact, or approximate formulas with the optimized parameters in symbolic form are preferred because powerful calculus methods can be applied to select the optimal parameters. The present paper is devoted to adequately choosing the parameters called structural sums, and corresponding analytical formulas. Such a formula is often asymptotic, and its correctly determined asymptotic precision shows its application area. We consider the question of the RVE size equivalent to the number of inclusions N per periodicity cell. It can be investigated numerically by solving a periodicity problem with N increasing up to stable effective constants not depending on N. Though one can find works in literature following these lines, they concern special distributions of inclusions with the numerical results performed for small N and for a small number of statistically investigated samples. A comprehensive study of 2D two-phase composites with equal circular inclusions is developed. It is demonstrated that using the concentration of inclusions and a contrast parameter is insufficient to properly study dispersed composites. The method of structural sums in combination with ML to improve model accuracy is applied. Based on the study, a new approach is suggested for selecting optimal parameters to analyze and classify two-dimensional dispersed composite structures. The included content fits 2020 Mathematics Subject Classification: 74Q15, 74-10.