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

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