A temporal graph neural network for cross-scale modelling of polycrystals considering microstructure interaction

Abstract

Machine learning (ML) based methods have achieved preliminary success in the constitutive modeling for single crystals or homogenized polycrystals with remarkable computational efficiency. However, existing ML-based constitutive models neglect grain-level anisotropy, which limits the accurate analysis of local effects. In the current work, a temporal graph neural network (TGNN) model is proposed to simulate cross-scale deformation behaviors of polycrystals under complex loading conditions, with straightforward consideration of microstructure variation and local interaction. The TGNN-based model, a variant of Linearized Minimal State Cells (LMSCs), extends its scope from macroscopic stress response to the mechanical response and orientation evolution of all grains within the aggregate. Specifically, the polycrystalline microstructure is represented with a graph to incorporate essential features of grains, including the spatial connectivity, crystallographic orientation and deformation state. Graph neural network (GNN) is used to capture the spatial correlation of grains, and the features extracted by the GNN are further processed with LMSCs to account for the history-dependent deformation and microstructure evolution. Moreover, the representative volume element (RVE) simulation with crystal plasticity is performed to provide reliable datasets for model establishment. The proposed model demonstrates high efficiency, accuracy and self-consistency in predicting the strain-stress response and orientation evolution at the scale of both individual grain and the overall aggregate under complex loading cases, such as cyclic loading and arbitrary loading.