Convolutional Neural Network and Image Processing-Based Approach for Homogenization of Lattice Structures

Abstract

Abstract. The homogenization approach is widely used in lattice structure design to simplify modeling of complex geometries by representing them as simple solid elements in finite element analysis (FEA). Homogenized material properties are obtained through microscale analysis of a representative volume element (RVE). Several methods exist to compute effective properties, including beam theory, asymptotic homogenization, and the finite element method. FEA is commonly used for its ability to model arbitrary lattice geometries accurately. However, for complex structures, conventional FEA is computationally expensive, requiring extensive preprocessing and producing large stiffness matrices, which reduces efficiency in multiscale analysis and optimization. This study introduces an image-based machine learning framework for efficient microscale modeling of arbitrarily shaped lattice structures. Unlike traditional surrogate modeling approaches that rely solely on machine learning, the novelty of this method lies in maintaining consistency between physical modeling and machine learning representations. Specifically, the binary matrix obtained via image processing is used to generate the finite element model for asymptotic homogenization (AH)-based microscale analyses, whose outputs train a convolutional neural network (CNN). This eliminates the need for conventional mesh generation and ensures the network learns from physically consistent data. The CNN framework enables rapid and accurate prediction of effective material properties from image-based RVE representations. The developed CNN models predict the homogenized elastic properties with normalized mean absolute error below 2% and normalized mean squared error on the order of 10−4, while requiring only a fraction of the computational time associated with conventional finite element-based homogenization analyses.