Surrogate Computational Homogenization Enhanced by Partition‐of‐Unity RBF Interpolation With Decision Trees

Abstract

ABSTRACT This study enhances a framework of surrogate computational homogenization (SCH) using decision tree‐based partition‐of‐unity radial basis function (PU‐RBF) interpolation for three‐dimensional finite‐deformation two‐scale analysis. The method addresses the scalability limitation of global RBF interpolation for large numerical material test (NMT) datasets by partitioning the strain space into overlapping subdomains with a binary‐tree strategy and training local RBF interpolants blended by smooth partition‐of‐unity weights. This local‐global construction reduces training cost while preserving a continuously differentiable stress response, enabling consistent tangent evaluation in implicit finite element solvers. For hyperelastic composite unit‐cell problems, the SCH model is trained with datasets exceeding samples, reconstructs database responses with high fidelity, and reproduces ‐level trends in both macroscopic and localization analyses with improved computational efficiency. Because it is nonintrusive at the constitutive‐update level, the surrogate is straightforward to integrate into standard CAE workflows. The present model is interpolation‐based and therefore intended for deformation states covered by the training data.