Phase-field modeling of brittle fracture problems with adaptive mesh refinement enhanced by time-series forecasting

Abstract

Modeling the propagation of cracks in brittle fracture problems is a complex process and often takes a long time to complete. This research study utilizes the phase-field approach coupled with an adaptive mesh algorithm to model crack propagation. Furthermore, we aim to accelerate the computational process by combining it with time-series forecasting techniques, namely ARIMA and LSTM. The single edge notched tensile and shear tests are used as a benchmark for the numerical model. The values of the phase-field variable, which demonstrated the crack, are collected from different mesh sizes. By interpreting these phase field values as a time-series, both ARIMA and LSTM model are employed to predict their values in the subsequent mesh refinement, relying on their values in the prior coarser mesh level. The outcomes reveal that both ARIMA and LSTM effectively forecast crack propagation and reduce computational time compared to exclusively employing a mathematical simulation model. The research also presents an evaluation of the merits and limitations inherent in both forecasting methods. Overall, LSTM proves to be better than ARIMA, as the method is more flexible, able to handle large amounts of data, and capable of extracting intricate relationships among data points within the series