PH-Net: Parallelepiped Microstructure Homogenization via 3D Convolutional Neural Networks (2201.09672v2)

Abstract: Microstructures are attracting academic and industrial interests with the rapid development of additive manufacturing. The numerical homogenization method has been well studied for analyzing mechanical behaviors 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 emerge as a more efficient choice but limit the microstructures into a cubic shape, which are infeasible to the periodic microstructures with a more general shape, e.g., parallelepiped. This paper introduces a fine-designed 3D convolutional neural network (CNN) for fast homogenization of parallel-shaped microstructures, named PH-Net. Superior to existing data-driven methods, PH-Net predicts the local displacements of microstructures under specified macroscope strains instead of direct homogeneous material, motivating 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 with hundreds of acceleration compared to the numerical homogenization method and even supports online computing. Moreover, it does not require a labeled dataset and thus is much faster than current deep learning methods in training processing. Benefiting from predicting local displacement, PH-Net provides both homogeneous material properties and microscopic mechanical properties, e.g., strain and stress distribution, yield strength, etc. We design a group of physical experiments and verify the prediction accuracy of PH-Net.