Convolutional Neural Networks for the Localization of Plastic Velocity Gradient Tensor in Polycrystalline Microstructures

Recent work has demonstrated the potential of convolutional neural networks (CNNs) in producing low-computational cost surrogate models for the localization of mechanical fields in two-phase microstructures. The extension of the same CNNs to polycrystalline microstructures is hindered by the lack of an efficient formalism for the representation of the crystal lattice orientation in the input channels of the CNNs. In this paper, we demonstrate the benefits of using generalized spherical harmonics (GSH) for addressing this challenge. A CNN model was successfully trained to predict the local plastic velocity gradient fields in polycrystalline microstructures subjected to a macroscopically imposed loading condition. Specifically, it is demonstrated that the proposed approach improves significantly the accuracy of the CNN models when compared with the direct use of Bunge–Euler angles to represent the crystal orientations in the input channels. Since the proposed approach implicitly satisfies the expected crystal symmetries in the specification of the input microstructure to the CNN, it opens new research directions for the adoption of CNNs in addressing a broad range of polycrystalline microstructure design and optimization problems.