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Forecasting phase-field variable in brittle fracture problems by autoregressive integrated moving average technique

Nguyen Cuong T., Le Long H., Dinh Minh H., La Ngoc M.

Computer Assisted Methods in Engineering and Science

2024

Vol. 31, no. 4

487--506

Phase-field modeling is a powerful and versatile computational approach for modeling the evolution of cracks in solids. However, phase-field modeling requires high computational cost for accurately capturing how cracks develop under increasing loads. In brittle fracture mechanics, crack initiation and propagation can be considered as a time series forecasting problem so they can be studied by observing changes in the phase-field variable, which represents the level of material damage. In this paper, we develop a rather simple approach utilizing the autoregressive integrated moving average (ARIMA) technique to predict variations of the phase-field variable in an isothermal, linear elastic and isotropic phase-field model for brittle materials. Time series data of the phase-field variable is extracted from numerical results using coarse finite-element meshes. Two ARIMA schemes are introduced to exploit the structure of the collected data and provide a prediction for changes in phasefield variable when using a finer mesh. This finer mesh gives a better results in terms of accuracy but requires significantly higher computational cost.