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

TL;DR

PH-Net is a novel 3D CNN model that efficiently predicts homogenized properties of parallelepiped microstructures, enabling fast, online microstructure analysis without extensive training data or shape restrictions.

Contribution

The paper introduces PH-Net, a 3D CNN for microstructure homogenization that handles general shapes, predicts local displacements, and offers significant speed improvements over traditional methods.

Findings

PH-Net achieves hundreds of times faster predictions than numerical homogenization.

It supports online computation and generalizes to various microstructure shapes and materials.

PH-Net accurately predicts both macroscopic properties and microscopic stress-strain distributions.

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.