Phase-Field Modelling of Brittle Fracture Using Time-Series Forecasting

The crack propagation behavior can be considered a time-series forecasting problem and can be observed based on the changes of the Phase-field variable. In this work, we study the behavior of the Isotropic Brittle Fracture Model (BFM), and propose a hybrid computational technique that involves a time-series forecasting method for finding results faster when solving variational equations with a fine-grained. We use this case study to compare and contrast two different time-series forecasting approaches: ARIMA, a statistical method, and LSTM, a neural network learning-based method. The study shows both methods come with different strengths and limitations. However, ARIMA method stands out due to its robustness and flexibility, especially when training data is limited because it can exploit a priori knowledge.