Application of AI and machine learning to the theory of composite materials

• Autorzy: Mityushev V. V. , Nurtazina K. B. , Nauryzbayev N. Zh.

Identyfikatory

DOI

10.62753/ctp.2025.06.1.1

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

artificial intelligence; machine learning; composite material; multiscale problem; microstructure; homogenization; structural sum

PL

sztuczna inteligencja; uczenie maszynowe; materiał kompozytowy; problem wieloskalowy; mikrostruktura; homogenizacja; suma strukturalna

• Wydawca: Polskie Towarzystwo Materiałów Kompozytowych
• Czasopismo: Composites Theory and Practice
• Rocznik: 2025
• Tom: R. 25, nr 1
• Strony: 11--20
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Mityushev V. V.

• Cracow University of Technology, Warszawska 24, 31-155Krakow, Poland

autor

Nurtazina K. B.

• L.N. Gumilyov Eurasian National University, 010008 Republic of Kazakhstan, Astana, Satpayev 2

autor

Nauryzbayev N. Zh.

• L.N. Gumilyov Eurasian National University, 010008 Republic of Kazakhstan, Astana, Satpayev 2

Bibliografia

• [1] Bakhvalov N.S., Panasenko G. (2012). Homogenisation: averaging processes in periodic media: mathematical problems in the mechanics of composite materials, 36. Springer Science & Business Media.
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• [3] Bensoussan A., Lions J.-L., Papanicolaou G. (2011). Asymptotic analysis for periodic structures. (Vol. 374). American Mathematical Soc.
• [4] Gonzalez R.C. (2009). Digital image processing. Pearson education India.
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• [6] Gluzman S., Mityushev V., Nawalaniec W. (2018). Computational Analysis of Structured Media. Academic Press, Elsevier, Amsterdam.
• [7] Drygaś P., Gluzman S., Mityushev V., Nawalaniec W. (2019). Applied analysis of composite media: analytical and computational results for materials scientists and engineers. Woodhead Publishing.
• [8] Torquato S. (2002). Random Heterogeneous Materials: Microstructure and Macroscopic Properties. SpringerVerlag, New York.
• [9] Mityushev, V., Nawalaniec, W. & Rylko, N. (2018). Introduction to mathematical modeling and computer simulations. Chapman and Hall/CRC.
• [10] Mityushev V. (2023). High-order contrast bounds for piezoelectric constants of two-phase fibrous composites.SIAM Journal on Multiscale Modeling and Simulation, 21(4), 1644-1666.
• [11] Weil A. (1999). Elliptic functions according to Eisenstein and Kronecker (Vol. 88). Springer Science & Business Media.
• [12] Mityushev V.. (2022). Effective properties of twodimensional dispersed composites. Part II. Revision of self-consistent methods. Computers & Mathematics with Applications, 121, 74-84. https://doi.org/10.1016/ j.camwa.2022.07.003
• [13] Mityushev V., Rylko N. (2012). Optimal distribution of the nonoverlapping conducting disks SIAM Journal on Multiscale Modeling and Simulation, 10(1), 180-190. https://doi.org/10.1137/110823225
• [14] Nawalaniec W. (2019). Classifying and analysis of random composites using structural sums feature vector. Proceedings of the Royal Society A, 475(2225).The Royal Society Publishing, 20180698. https://doi.org/ 10.1098/rspa.2018.0698
• [15] Torquato S. (2002). Random heterogeneous materials: microstructure and macroscopic properties. Appl. Mech. Rev., 55(4), B62-B63. https://doi.org/10.1115/1.1483342
• [16] Czapla R., Nawalaniec W., Mityushev, V. (2012). Effective conductivity of random two-dimensional composites with circular non-overlapping inclusions. Computational Materials Science, 63, 118-126. https://doi.org/10.1016/j.commatsci.2012.05.058

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).