Graph-enhanced deep material network: multiscale materials modeling with microstructural informatics

Abstract

This study addresses the fundamental challenge of extending the deep material network (DMN) to accommodate multiple microstructures. DMN has gained significant attention due to its ability to be used for fast and accurate nonlinear multiscale modeling while being only trained on linear elastic data. Due to its limitation to a single microstructure, various works sought to generalize it based on the macroscopic description of microstructures. In this work, we utilize a mechanistic machine learning approach grounded instead in microstructural informatics, which can potentially be used for any family of microstructures. This is achieved by learning from the graph representation of microstructures through graph neural networks. Such an approach is a first in works related to DMN. We propose a mixed graph neural network (GNN)-DMN model that can single-handedly treat multiple microstructures and derive their DMN representations. Two examples are designed to demonstrate the validity and reliability of the approach, even when it comes to the prediction of nonlinear responses for microstructures unseen during training. Furthermore, the model trained on microstructures with complex topology accurately makes inferences on microstructures created under different and simpler assumptions. Our work opens the door for the possibility of unifying the multiscale modeling of many families of microstructures under a single model, as well as new possibilities in material design.