Abstract
Rapid and accurate stress field prediction in heterogeneous material systems is critical fora variety of applications, including design optimization, uncertainty quantification, structural health monitoring, materials failure assessment, system control and decision-making. Physics-based simulations such as the finite element method provide high-fidelity predictions but can be computationally expensive and time consuming. On the other hand, data-driven approaches have the promise to rapidly predicting reliable results to meet real-time application constraints. In this study, different deep learning frameworks are applied and evaluated in predicting the high-dimensional stress field responses of heterogeneous materials. Two material models are considered: the first one is based on linear elastic materials while the second one involves nonlinear elastic-plastic materials. In the linear elastic model, the first framework employs a combination of model order reduction and artificial neural networks(ANN). The stress fields are first projected to a low-dimensional representation using a model order reduction technique of proper orthogonal decomposition (POD). After that, ANN issued to predict full-field responses based on POD reduced modes. The second framework is based on a deep Resnet-based Convolutional Neural Network, while the third one is based on a conditional Generative Adversarial Network. Two numerical examples are analyzed to evaluate the above frameworks. The first is a panel containing a heterogeneous material inclusion varying in terms of position and size. The reconstructed POD fields using ANN provide accurate predictions overall but more deviations appear when the inclusion is small or close to the boundary. On the other hand, CNN and cGAN approaches give more accurate and robust predictions. In the second example, a plate with a hole that varies in position and size is considered. Both CNN and cGAN models accurately captured stress concentrations as well as the full stress fields, while cGAN give better predictions in validations of unseen datasets. In the elastic-plastic model, a plate with multiple holes is considered. Convolutional Long Short Term Memory based CNN framework is implemented to capture the time evolution of the stress field as well as the deformation of holes. The above deep learning frameworks show remarkable potentials in predicting full-field responses for a variety of heterogeneous materials.