2019 Fiscal Year Research-status Report
Theoretical and numerical analysis for a phase-field model describing the crack growth phenomenon
| Project/Area Number |
19K14605
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| Research Institution | National Institute of Advanced Industrial Science and Technology |
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Principal Investigator |
GAO Yueyuan 国立研究開発法人産業技術総合研究所, 材料・化学領域, 産総研特別研究員 (80807793)
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| Project Period (FY) |
2019-04-01 – 2021-03-31
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| Keywords | Phase-field model / Finite volume method / Crack growth phenomenon / Numerical analysis |
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| Outline of Annual Research Achievements |
The crack growth phenomenon is irreversible and mathematically such unidirectional evolution processes are often described by partial differential equations involving the positive-part function. By numerical and theoretical study of a phase-field model, this project expects to give better understanding of the effect of the positive-part function on partial differential equations and to give validation to the phase-field model so that it can be applied to other research topics related the crack growth phenomenon in materials science. We advanced the project as planned in numerical and theoretical aspects. This project helps me to develop further research subject in applied mathematics and material sciences.
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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
We advanced the project as planned in numerical and theoretical aspects. Numerically, we performed simulations for the phase-field model describing the crack growth. We calculated the J-integral which can represent the toughness of the material. The robustness of codes can be relayed on. Theoretically, we have learnt and understand the proof the existence and uniqueness of the Allen-Cahn equation and diffusion equation with the positive part operator. We plan to advance to the phase-field system and we consider the convergence of the numerical scheme. Yet as the project is going on, we spent some time in understanding of the physical background. We spent some time to obtain the correct way to compute the J-integral. Those are the reasons that the advancement of the project is in Status 2.
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| Strategy for Future Research Activity |
This year, we continue the project with more different aspects. We continue the numerically study on the speed of the crack propagation by setting the material length long enough; there could be a connection between the speed and the toughness of the material. Travelling wave solution could be another approach. And then we consider materials with random inhomogeneity. There may be an inherit connection between the J-integral value and the statistical properties of the randomness such as the expectation and the variances. And theoretically we will investigate the convergence of the numerical scheme for the original system in the deterministic case. We may then continue the study to system with stochasticity, either as the inhomogeneity or as the perturbation of a noise.
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| Causes of Carryover |
The project will be carried on by simulations on computers and as the project is going on, we will have more interaction and discussion with other researchers and making presentations. Therefore, for next fiscal year, one part of the funding will be used for purchasing numerical tool software such as Matlab and the other part will be used for business trips of scientific visits and of presentations in conferences.
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Research Products
(2 results)
