An enhanced sub-clustering based self-consistent clustering analysis for efficient homogenization of thermal conductivity in woven composites

This study proposes an enhanced self-consistent clustering analysis (SCA) framework for predicting the effective thermal conductivity of composite materials. We first rigorously derive the periodic Lippmann–Schwinger equation to model heat transfer in heterogeneous media and establish a numerically robust solution scheme using the Fourier spectral method. Subsequently, a cluster-based discretization of the Lippmann–Schwinger equation is developed, integrated with a two-stage offline-online computational framework. A self-consistent updating scheme is implemented to achieve fast updates of the reference medium and interaction tensor, enabling rapid homogenization of thermal conductivity in heterogeneous materials. Furthermore, a sub-clustering method is introduced to extend the applicability of traditional static SCA, which is typically limited to fixed geometry and material configurations, two scenarios involving microstructures with similar geometry and varying material configurations. The accuracy and computational efficiency of the proposed framework are systematically validated via multiscale thermal conductivity homogenization analyses of plain woven composites. Results demonstrate that the method retains the computational speed advantages of cluster-based reduced-order models while achieving numerical accuracy comparable to direct Fourier spectral solutions. Using this framework, a comprehensive database of woven composite microstructures is generated and complemented by an artificial neural network (ANN) surrogate model. The ANN model facilitates rapid multiscale prediction of effective thermal conductivity, validating the practical utility of the approach for engineering applications requiring efficient analysis in composite design and optimization.