A Physics-Informed General Convolutional Network for the Computational Modeling of Materials With Damage

Despite their effectiveness in modeling complex phenomena, the adoption of machine learning (ML) methods in computational mechanics has been hindered by the lack of availability of training datasets, limitations on the accuracy of out-of-sample predictions, and computational cost. This work presents a physics-informed ML approach and network architecture that addresses these challenges in the context of modeling the behavior of materials with damage. The proposed methodology is a novel physics-informed general convolutional network (PIGCN) framework that features (1) the fusion of a dense edge network with a convolutional neural network (CNN) for specifying and enforcing boundary conditions and geometry information, (2) a data augmentation approach for learning more information from a static dataset that significantly reduces the necessary data for training, and (3) the use of a CNN for physics-informed ML applications, which is not as well explored as graph networks in the current literature. The PIGCN framework is demonstrated for a simple two-dimensional, rectangular plate with a hole or elliptical defect in a linear-elastic material, but the approach is extensible to three dimensions and more complex problems. The results presented in this article show that the PIGCN framework improves physics-based loss convergence and predictive capability compared to ML-only (physics-uninformed) architectures. A key outcome of this research is the significant reduction in training data requirements compared to ML-only models, which could reduce a considerable hurdle to using data-driven models in materials engineering where material experimental data are often limited.