Lattice Structure Design Using Machine Learning and Homogenization Approach

The homogenization approach is commonly used for lattice structure design by simplifying the modeling of complex geometric structures using simple solid elements in the finite element analysis. Homogenized material properties for solid elements are obtained through a Representative Volume Element (RVE). Several homogenization methods are available to determine effective material properties, including beam theory asymptotic homogenization (AH) and various others. In the current study, AH is chosen as it is widely utilized to assess lattice mechanical properties for a wide range of shapes. Although this approach is popular, it requires fine meshes when analyzing complex lattice geometries for computing material properties using finite element methods. Thus, it increases modeling complexity by including model preprocessing and generates a large order stiffness matrix, resulting in a computationally expensive analysis. Therefore, this study incorporated image processing instead of traditional mesh generation for calculating effective material properties. This methodology converts any image of a random-shaped RVE into a binary matrix to calculate its properties. In addition, this study introduced a Convolutional Neural Network (CNN) based on images of square lattice RVEs, which allows accurate and fast predictions of material properties. The developed model showed an error of 1.60% estimated on Mean Absolute Error (MAE) and 0.08% based on Mean Squared Error (MSE) in the training phase.