A hybrid micromechanical-based symbolic regression model for transverse effective conductivity of high-contrast component composites

• Published in: Archive of applied mechanics (1991) Vol. 95; no. 8
• Main Authors: Vu, Viet-Hung, Le, Ba-Anh, Tran, Bao-Viet, Bui, Thi-Loan, Nguyen, Van-Hao
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 02.08.2025; Springer Nature B.V
• Subjects: Classical Mechanics; Composite materials; Engineering; Genetic algorithms; Inclusions; Mathematical analysis; Original; Parameters; Regression models; Theoretical and Applied Mechanics; Effective conductivity; Finite element method; Symbolic regression; Micromechanical approach; Genetic programming; Machine learning approach
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-025-02902-8

In the context of combining analytical models with data driven, this paper aims to establish an appropriate computational process for constructing hybrid formulas to predict the transverse effective conductivity of uniaxial composites. Specifically, the paper predicts the geometric parameter r, which represents the size of a pattern shape in the generalized self-consistent approximation model and could characterize the complexity of the material structure. For the case of a random suspension of fibers, the parameter r can be represented by a ReLU function that allows variation from 1 to 0 as the structure transitions from sparse (central symmetry) to dense (hexagonal structure). For ordered structured configurations, database are constructed for two cases: square and hexagonal arrays. Then, a calculation strategy is proposed based on the genetic programming model to find the most suitable analytical formula for each structure. The resulting models show excellent agreement with both numerical and analytical results, even in cases where the volume fraction approaches the theoretical maximum of 99.9% and the conductivity of the inclusions tends toward infinity. The method is also validated with available experimental data in the most extreme case and further extended to the polydisperse scenario, producing stable and accurate results. The computational process thus holds great potential for extension to various models and different types of composite materials.