  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.
