Crystallographic Texture-Generalizable Orientation-Aware Interaction-Based Deep Material Network for Polycrystal Modeling and Texture Evolution

TL;DR

The paper tackles transferability in texture-aware polycrystal modeling by extending ODMN with Texture-Adaptive Clustering and Sampling (TACS) and a Graph Neural Network (GNN). This TACS-GNN-ODMN framework enables predicting both nonlinear mechanical responses and texture evolution for unseen crystallographic textures without retraining, while preserving physical interpretability via the ODMN hierarchy. It demonstrates high fidelity against DNS across cyclic and shear loading, and provides a tunable depth parameter N to balance accuracy and speed. The approach delivers substantial accuracy and orders-of-magnitude speedups, offering a robust surrogate for multiscale simulations and design of textured polycrystals.

Abstract

Machine learning has significantly advanced materials modeling by enabling surrogate models that achieve high computational efficiency without compromising predictive accuracy. The Orientation-aware Interaction-based Deep Material Network (ODMN) is one such framework, in which a set of material nodes represents crystallographic textures, and a hierarchical interaction network enforces stress equilibrium among these nodes based on the Hill-Mandel condition. Using only linear elastic stiffness data, ODMN learns the intrinsic geometry-mechanics relationships within polycrystalline microstructures, allowing it to predict nonlinear mechanical responses and texture evolution with high fidelity. However, its applicability remains limited by the need to retrain for each distinct crystallographic texture. To address this limitation, we introduce the TACS-GNN-ODMN framework, which integrates (i) a Texture-Adaptive Clustering and Sampling (TACS) scheme for initializing texture-related parameters and (ii) a Graph Neural Network (GNN) for predicting stress-equilibrium-related parameters. The proposed framework accurately predicts nonlinear responses and texture evolution across diverse textures, showing close agreement with direct numerical simulations (DNS). By eliminating the requirement for texture-specific retraining while preserving physical interpretability, TACS-GNN-ODMN substantially enhances the generalization capability of ODMN, offering a robust and efficient surrogate model for multiscale simulations and next-generation materials design.

Figures (14)

• Figure 1: Workflow of the TACS–GNN–ODMN framework. In the offline training stage, polycrystalline RVEs are generated and converted into graphs for GNN-based prediction of micromechanical equilibrium parameters, while TACS provides initialization for texture-related parameters. In the online prediction stage, an unseen RVE is processed to construct a standalone ODMN surrogate, enabling rapid prediction of homogenized responses and texture evolution.
• Figure 2: Schematic architecture of the ODMN. A binary-tree material network defines the hierarchical stress-equilibrium interactions, while the $2^N$ material nodes represent RVE subdomains characterized by local orientations and weighting factors.
• Figure 3: Architecture of the GNN module for predicting ODMN micromechanical equilibrium parameters. A grain-level microstructure graph is processed by two GATv2Conv layers with ReLU activations, followed by global mean pooling and a fully connected layer with Softplus activation to output the angular parameters $\{\theta^{l}_{p}, \phi^{l}_{p}\}$ of the material network.
• Figure 4: Training and validation error curves of the TACS–GNN–ODMN framework with $N = 7$.
• Figure 5: Unseen RVEs used for testing: (a) S1, (b) S2, (c) W1, (d) W2.