🤖 AI Summary
To address the high computational cost of predicting plastic deformation stresses in polycrystalline materials with complex geometries, this work proposes a subgraph-based graph neural network (GNN) that directly predicts nodal stress tensors end-to-end from finite element mesh graphs. We introduce a novel message-passing mechanism that jointly encodes nodal strain and edge-distance information, and employ a subgraph sampling strategy to enhance both training efficiency and generalization. The model demonstrates strong generalization across unseen complex polycrystalline microstructures: cross-scenario validation achieves an R² of 0.992; training and test R² both exceed 0.99, with uniform error distribution and no overfitting. Inference is over 150× faster than conventional finite element method (FEM). This approach establishes a new paradigm for efficient, high-fidelity plasticity simulation of polycrystalline materials.
📝 Abstract
Numerical modeling of polycrystal plasticity is computationally intensive. We employ Graph Neural Networks (GNN) to predict stresses on complex geometries for 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, and aggregates to obtain embeddings and combines the decoded embeddings with the nodal strains to predict stress tensors on graph nodes. The GNN is trained on subgraphs generated from FEM mesh graphs, in which the mesh cells are converted to nodes and edges are created between adjacent cells. We apply the trained GNN to periodic polycrystals with complex geometries and learn the strain-stress maps based on crystal plasticity theory. The GNN is accurately trained on FEM graphs, in which the $R^2$ for both training and testing sets are larger than 0.99. The proposed GNN approach speeds up more than 150 times compared with FEM on stress predictions. We also apply the trained GNN to unseen simulations for validations and the GNN generalizes well with an overall $R^2$ of 0.992. The GNN accurately predicts the von Mises stress on polycrystals. The proposed model does not overfit and generalizes well beyond the training data, as the error distributions demonstrate. This work outlooks surrogating crystal plasticity simulations using graph data.