Learning polycrystal plasticity using mesh-based subgraph geometric deep learning

Polycrystal plasticity in metals is characterized by nonlinear behavior and strain hardening, making numerical models computationally intensive. We employ Graph Neural Network (GNN) to surrogate polycrystal plasticity from finite element method (FEM) simulations. We present a novel message-passing GNN that encodes nodal strain and edge distances between FEM mesh cells, aggregates them to obtain embeddings, and combines the decoded embeddings with the nodal strains to predict stress tensors on graph nodes. We demonstrate training GNN based on subgraphs generated from FEM mesh-graphs, in which the mesh cells are converted to nodes and edges are created between adjacent cells. The GNN is trained on 72 graphs and tested on 18 graphs. We apply the trained GNN to periodic polycrystals and learn the stress-strain maps based on strain-gradient plasticity theory. The GNN is accurately trained based on FEM graphs, in which the $R^2$ for both training and testing sets are 0.993. The proposed GNN plasticity constitutive model speeds up more than 150 times compared with the benchmark FEM method on randomly selected test polycrystals. We also apply the trained GNN to 30 unseen FEM simulations and the GNN generalizes well with an overall $R^2$ of 0.992. Analysis of the von Mises stress distributions in polycrystals shows that the GNN model accurately learns the stress distribution with low error. By comparing the error distribution across training, testing, and unseen datasets, we can deduce that the proposed model does not overfit and generalizes well beyond the training data. This work is expected to pave the way for using graphs as surrogates in polycrystal plasticity modeling.