Homogenization and artificial neural network prediction of elastic properties in triply periodic minimal surface structures

Abstract This study introduces a comprehensive framework for the generation, homogenization, and prediction of linear elastic properties of Triply Periodic Minimal Surface (TPMS)-based unit cells. Hybrid cells are created by combining four fundamental TPMS structures, namely primitive, gyroid, diamond, and I-WP. Finite element analysis is used to calculate the equivalent elastic properties of these structures. A dataset is generated using a full-factorial design of the experiment approach to train an Artificial Neural Network (ANN) for predicting the coefficients of the equivalent stiffness matrix. Findings demonstrate that the network can provide an accurate estimation of the elastic properties, thus significantly improving the efficiency of the design process. Particularly, the performances of the ANN overcome those of the Gibson-Ashby model in the orthotropic modeling of the cell. More importantly, the ANN is able to capture the anisotropy that arises by mixing the fundamental equations, thus allowing for an accurate representation of the actual behavior of the structure. This work contributes to the advancement of high-performance, lightweight materials, providing a robust and efficient methodology for the design of new structures to be produced via additive manufacturing.