Deep learning phase-field model for brittle fractures

We present deep learning phase-field models for brittle fracture. A variety of physics-informed neural networks (PINNs) techniques, for example, original PINNs, variational PINNs (VPINNs), and variational energy PINNs (VE-PINNs) are utilized to solve brittle phase-field problems. The performance of the different versions is investigated in detail. Also, different ways of imposing boundary conditions are examined and are compared with a self-adaptive PINNs approach in terms of computational cost. Furthermore, the data-driven discovery of the phase-field length scale is examined. Finally, several numerical experiments are conducted to assess the accuracy and the limitations of the discussed deep learning schemes for crack propagation in two dimensions. We show that results can be highly sensitive to parameter choices within the neural network.