Deep Learning–Based Surrogates for Efficient Phase-Field Modeling of Stochastic Quasi-Brittle Materials

The random microstructure of quasi-brittle materials causes significant uncertainty in their macroscopic properties. The stochastic analysis is crucial for understanding issues related to material strength, deformation, and failure. A deep learning surrogate model for the stochastic analysis of quasi-brittle materials is developed to address computational challenges posed by stochastic finite element method (SFEM) and Monte Carlo modeling. Material randomness is first described by using a stochastic harmonic function method to generate random fields. Phase-field models are then integrated with SFEM to reduce the spurious mesh sensitivity. Stress–strain data from phase-field simulations are used to train the deep learning–based surrogate models, which incorporates a convolutional neural network (CNN) and transformer. Through testing, the CNN model is selected as the surrogate model, with an R2 value of 0.9909 for the training set and 0.9884 for the testing set, demonstrating its accuracy in predicting material behavior. It is also demonstrated in the case studies that the proposed deep learning–based surrogate model significantly reduces computational costs when comparing with SFEM in Monte Carlo modeling.