PH-Net: Parallelepiped microstructure homogenization via 3D Convolutional Neural Networks

Microstructures are attracting academic and industrial interest because of the rapid development of additive manufacturing. The numerical homogenization method has been well studied for analyzing mechanical behav-iors of microstructures; however, it is too time-consuming to be applied to online computing or applications requiring high-frequency calling, e.g., topology optimization. Data-driven homogenization methods are consid-ered a more efficient choice but the microstructures are limited to cubic shapes, therefore are unsuitable for periodic microstructures with a more general shape, e.g., parallelepipeds. This paper introduces a fine-designed 3D convolutional neural network (CNN) for fast homogenization of parallelepiped microstructures, named PH -Net. Superior to existing data-driven methods, PH-Net predicts the local displacements of microstructures under specified macroscopic strains instead of direct homogeneous material, empowering us to present a label-free loss function based on minimal potential energy. For dataset construction, we introduce a shape-material transformation and voxel-material tensor to encode microstructure type, base material and boundary shape together as the input of PH-Net, such that it is CNN-friendly and enhances PH-Net on generalization in terms of microstructure type, base material, and boundary shape. PH-Net predicts homogenized properties hundreds of times faster than numerical homogenization and even supports online computing. Moreover, it does not require a labeled dataset and thus the training process is much faster than current deep learning methods. Because it can predict local displacement, PH-Net provides both homogeneous material properties and microscopic mechanical properties, e.g., strain and stress distribution, and yield strength. We also designed a set of physical experiments using 3D printed materials to verify the prediction accuracy of PH-Net.