Stress Predictions in Polycrystal Plasticity using Graph Neural Networks with Subgraph Training

TL;DR

This paper introduces a novel graph neural network approach to predict stresses in polycrystal plasticity efficiently, achieving high accuracy and significant speedup over traditional FEM simulations.

Contribution

A new message-passing GNN model that encodes FEM mesh data for stress prediction in polycrystals, demonstrating high accuracy and generalization.

Findings

GNN achieves R^2 > 0.99 on training and testing data.

GNN speeds up stress prediction by over 150 times compared to FEM.

Model generalizes well to unseen simulations with R^2 of 0.992.

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.