Variational Machine Learning Method for Simulation of Fracture Mechanics

In the last few decades, Machine Learning has experienced rapid growth thanks to the development of hardware technologies, and the improvement of optimization algorithms, and computational capabilities. It found space in a variety of businesses, such as in the engineering field, where several neural network architectures can be employed, enabling the processing of a huge amount of data and solving complex problems, such as solving partial differential equations. That is noteworthy since the partial differential equations constitute the governing laws to model the physics behind most engineering problems. Their solution is crucial for understanding the behavior of the systems, but usually is complex and requires advanced computational techniques. In this context is located fracture mechanics, the field of study that examines and predicts how cracks propagate through the structures, to understand how and when failure occurs. The current work aims to simulate fracture in two bi-dimensional plates by exploiting the potential of neural networks. The study is carried out using Variational Physics-Informed Neural Networks. This type of structure includes the governing equations directly into its architecture, guaranteeing their fulfillment and proving their suitability to investigate the phenomenon. To study the fracture behavior, the phase-field model is adopted, which is based on a global energy approach. Therefore, the Deep Energy Method is employed to approximate the solution of the differential equations characterizing the phase field model. In this innovative approach the loss function that get minimized is the overall energy of the system. The results so obtained are compared with the FEM simulation ones, conducted using COMSOL Multiphysics software and adopting the phase-field method. Consequently, the capabilities and the criticalities of the neural network model are highlighted. The first study investigated a mode I fracture and revealed a good level of accuracy in the results predicted by the neural network. Indeed, both the damage and displacement fields are well approximated once the model parameters have been tuned. However, this level of accuracy significantly affects computational times. It was therefore shown that it is possible to obtain reasonable results in a shorter computational time by sacrificing some accuracy. The second study highlighted the capability of the neural network to track a mixed mode I-II fracture. The crack path is outlined, but some differences come out in the field distribution. However, the computational time is extremely short, making this approach convenient. This study shows that neural networks have great potential in fracture mechanics, as they can provide a fairly accurate estimate of fracture propagation. The results of this project are promises for further developments in the future.