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Microstructures are attracting academic and industrial interests with therapid development of additive manufacturing. The numerical homogenizationmethod has been well studied for analyzing mechanical behaviors ofmicrostructures; however, it is too time-consuming to be applied to onlinecomputing or applications requiring high-frequency calling, e.g., topologyoptimization. Data-driven homogenization methods emerge as a more efficientchoice but limit the microstructures into a cubic shape, which are infeasibleto the periodic microstructures with a more general shape, e.g.,parallelepiped. This paper introduces a fine-designed 3D convolutional neuralnetwork (CNN) for fast homogenization of parallel-shaped microstructures, namedPH-Net. Superior to existing data-driven methods, PH-Net predicts the localdisplacements of microstructures under specified macroscope strains instead ofdirect homogeneous material, motivating us to present a label-free lossfunction based on minimal potential energy. For dataset construction, weintroduce a shape-material transformation and voxel-material tensor to encodemicrostructure type,base material and boundary shape together as the input ofPH-Net, such that it is CNN-friendly and enhances PH-Net on generalization interms of microstructure type, base material, and boundary shape. PH-Netpredicts homogenized properties with hundreds of acceleration compared to thenumerical homogenization method and even supports online computing. Moreover,it does not require a labeled dataset and thus is much faster than current deeplearning methods in training processing. Benefiting from predicting localdisplacement, PH-Net provides both homogeneous material properties andmicroscopic mechanical properties, e.g., strain and stress distribution, yieldstrength, etc. We design a group of physical experiments and verify theprediction accuracy of PH-Net.

PH-Net: Parallelepiped Microstructure Homogenization via 3D Convolutional Neural Networks