DH-Net: Deformed Microstructure Homogenization via 3D Convolutional Neural Networks

With the rapid development of additive manufacturing, microstructures are attracting both academic and industrial interests. As an efficient way of analyzing the mechanical behaviors of microstructures, the homogenization method has been well studied in the literature. However, the classic homogenization method still faces challenges. Its computational cost is high for topological optimization that requires highly repeated calculation. The computation is more expensive when the microstructure is deformed from a regular cubic, causing changes for the virtual homogeneous material properties. To conquer this problem, we introduce a fine-designed 3D convolutional neural network (CNN), named DH-Net, to predict the homogenized properties of deformed microstructures. The novelty of DH-Net is that it predicts the local displacement rather than the homogenized properties. The macroscopic strains are considered as a constant in the loss function based on minimum potential energy. Thus DH-Net is label-free and more computation efficient than existing deep learning methods with the mean square loss function. We apply the shape-material transformation that a deformed microstructure with isotropic material can be bi-transformed into a regular structure with a transformed base material, such that the input with a CNN-friendly form feeds in DH-Net. DH-Net predicts homogenized properties with hundreds of acceleration compared to the standard homogenization method and even supports online computing. Moreover, it does not require a labeled dataset and thus can be much faster than current deep learning methods in training processing. DH-Net can predict both homogenized material properties and micro-mechanical properties, which is unavailable for existing DL methods. The generalization of DH-Net for different base materials and different types of microstructures is also taken into account.