Computational Strategy for Analyzing Effective Properties of Random Composites–Part III: Machine Learning

This paper continues the analysis from Parts I and II, which addressed two-dimensional dispersed random composites. This part extends previous analytical studies by incorporating machine learning (ML) methods to quantitatively classify microstructures. The methodology relies on decomposing the expressions for the effective tensors into geometrical and physical parts, represented by structural sums and component-specific physical constants. The study concerns a two-phase composite with non-overlapping circular inclusions embedded in an isotropic elastic matrix. The random distribution of inclusions ensures macroscopic isotropy of the composite. A key outcome is the explicit demonstration of how the effective tensor depends on the geometric probabilistic distributions of inclusions and the computational protocols employed in their realization. These steps constitute the strategy for studying elastic fibrous composites, classifying them by macroscopic properties, and describing an analytical algorithm to derive expressions for computing the effective constants. The decomposition theorem and the construction of feature vectors consisting of structural sums are used as inputs to the ML analysis. As a result, we develop a computationally effective strategy to classify dispersed random composites indistinguishable by simple observations.