Data-driven methods for stress field predictions in random heterogeneous materials

Predicting full-field stress responses is of fundamental importance to assessing materials failure and has various engineering applications in design optimization, manufacturing process control, and structural health monitoring. This article develops and evaluates different data-driven methods for efficient and accurate predictions of full stress fields in random heterogeneous materials. The first approach integrates model order reduction of proper orthogonal decomposition (POD) with classical machine learning techniques (K-nearest neighbors, random forest, and artificial neural networks) to predict full-field responses based on POD-reduced coefficients. However, this strategy shows limitations in predicting full stress fields, especially for heterogeneous material inclusions of small size or being close to the domain boundary. After that, two computer vision-based deep learning approaches were developed for full-field predictions. The first one uses a Resnet-based Convolutional Neural Network (CNN), and the second is based on a modified conditional Generative Adversarial Network (cGAN). Two representative example problems were studied: a random heterogeneous material inclusion or a void varying in size and location. In contrast to POD-based classical machine learning, almost invisible differences were found between the entire stress fields in finite element simulations and computer vision-based deep learning (CNN/cGAN) predictions, with significantly reduced mean squared error (MSE) and correlation values (R2) mostly above 0.99. On the other hand, the proposed cGAN provides more accurate predictions than CNN with fewer epochs.