Theoretical and numerical analysis for a phase-field model describing the crack growth phenomenon
| Project/Area Number |
19K14605
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Hokkaido University (2021-2022)
National Institute of Advanced Industrial Science and Technology (2019-2020) |
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Principal Investigator |
GAO Yueyuan 北海道大学, 電子科学研究所, 特任助教 (80807793)
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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| Project Status |
Granted (Fiscal Year 2022)
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| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | Crack growth phenomenon / Phase-field models / Inverse problem / Inhomogeneity / Fracture toughness / Phase-field Model / Inverse estimation / Data science / Phase-field model / Numerical analysis / Finite volume method |
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| Outline of Research at the Start |
The research of this project is based on the phase-field model by Takaishi and Kimura which describes the crack growth phenomenon in materials science. The model is a partial differential equations system involving the positive-part function. We study the connection between the structure of the material in deterministic and stochastic cases and the toughness of the material. We perform numerical simulations by finite volume methods and investigate the well-posedness of the system by means of the convergence of the numerical scheme.
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| Outline of Annual Research Achievements |
In this project, we first study the crack propagation in an inhomogeneous media in which fracture toughness varies in space. By using the two phase-field models based on two different surface energy functionals, which are so called AT1 and AT2 models, we perform simulations of the crack propagation and show that the J-integral reflects the effective inhomogeneous toughness. We then formulate inverse problems to estimate space-dependent fracture toughness from the crack path. Our method which is based on data pre-processing and regression, successfully estimates the positions and magnitude of tougher regions. We also demonstrate that our method works for different geometry of inhomogeneity.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
After having brought up the idea of the data pre-processing, that is sampling in the region where the crack has not arrived, during the academic year 2022-2023, we have been applying this idea to different inhomogeneous materials in both AT1 and AT2 models.
After having showed the results that our method works for both models and also the difference among the 2 models, we present the detailed explanation of the inherent difference of the 2 models. We have well summarized the results and submitted the corresponding paper. The paper is accepted for publication in the journal Physica D: Nonlinear Phenomena.
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| Strategy for Future Research Activity |
The paper has well summarized the novelty and the main results of the project. As for the limitation of our study, currently, we have supposed that the phase-field model of strain field and the crack field is known and the parameters except the fracture toughness are known. This limitation leads the research to future study, such as to treat the strain field as a hidden variable and to apply other methods to estimate the model as well as some other parameters at the same time.
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Report
(4 results)
Research Products
(10 results)
