Forecasting phase-field variable in brittle fracture problems by autoregressive integrated moving average technique
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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute of Fundamental Technological Research Polish Academy of Sciences
2024-12-01
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| Series: | Computer Assisted Methods in Engineering and Science |
| Subjects: | |
| Online Access: | https://cames.ippt.pan.pl/index.php/cames/article/view/1697 |
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| Summary: | 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.
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| ISSN: | 2299-3649 2956-5839 |