A physics-constrained neural network for crystal plasticity modelling of FCC materials

In the current work, a physics-constrained neural network is coupled with the crystal plasticity theory to predict the grain-level responses in FCC material. Based on the crystal plasticity, the shear strain rate of slip system is identified as the key feature, and the physical constitutive equations of crystal plasticity are encoded into the loss function. A data augmentation considering the slip shear direction enables the model to learn the reverse loading in constitutive relations. The introduced physics-constraints accelerate neural network model convergence and promotes prediction accuracy, especially for small-scale dataset. The transfer learning is performed on the model by leveraging the constitutive equations learned from the base dataset with linear biaxial loading to complex strain paths with a small-scale extended dataset. This approach significantly reduces the requirement of data quantity and accurately captures the complex in-plane deformation of crystals with any initial orientations, including cyclic loading and arbitrary non-monotonic loading.