2016 Fiscal Year Research-status Report
Bridging across mathematical analysis, probability and materials mechanics for a better modeling of martensitic microstructure and defects.
| Project/Area Number |
16K21213
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| Research Institution | Kyushu University |
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Principal Investigator |
Cesana Pierluigi 九州大学, マス・フォア・インダストリ研究所, 准教授 (60771532)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | Gamma-Convergence / Dimension-reduction / phase-transformations / avalanches / stochastic process |
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| Outline of Annual Research Achievements |
Accomplished the analysis and modeling of thin elastic membranes of an active material (nematic elastomers). Determined the compactness properties of the minimizing sequences and computed the effective asymptotic energy of the “sandwich” structure by means of Gamma-Convergence. Currently finalizing the paper.
Stochastic modeling of martensite microstructure and avalanches. Accomplished the 3-Dimensional analysis of a fragmentation process describing the nucleation and evolution of plates. Obtained analytical solutions and numerical approximations of the distributions of plates describing a martensitic microstructure observed in phase-transforming materials in metallurgy (elastic crystals).
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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
First paper regarding the modeling and analysis of thin elastic membranes has been developed throughout the first year and has now come to completion. Currently I am wrapping up a manuscript in collaboration with Dr. Andres Baldelli (ENSTA, Paris). More work is to be done in other directions (either analysis, modeling, numerics or all) and will be the object of another paper. First paper regarding stochastic models of martensitic avalanches is almost finished. Very little work needs to be finalized (such as, some numerical simulations to validate some 2D analytical results) although the main part (3D analysis) has been accomplished. Currently am finishing the work and together with my collaborator Prof. Ben Hambly (Oxford) we have already started wrapping up the paper.
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| Strategy for Future Research Activity |
Finalizing the 2 papers started during the First year. Further work to be done includes: 1 Construction of Boundary Value Problems for thin structures of nematic elastomers and computation of their solution, by either analytical or numerical methods and comparison with experimental evidence.
2 To construct and refine a platform of flexible stochastic models for the evolution of plates. Creation of more physically sound and sophisticated models taking into account surface energy penalization and other phenomena. Accomplish numerical analysis of the models where it is not possible to obtain closed form equations.
3 Possibly compare analytical and numerical results with experimental data of martensitic avalanches and disclinations.
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| Causes of Carryover |
didn't need to use the Kakenhi money for equipment (PC or books)
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| Expenditure Plan for Carryover Budget |
will use in the following year for either travel, equipment or inviting an international scientist.
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