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 Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
Materials/Mechanics of materials
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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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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | Non-linear analysis / Materials Science / Gamma-convergence / Stochastic processes / Elasticity Theory / Non-linear PDEs / Calculus of Variations / Shape-Memory Alloys / Lattice defects / Nematic Elastomers / Probabilistic modeling / Gamma-Convergence / Dimension-reduction / phase-transformations / avalanches / stochastic-process / stochastic process / Nonlinear Analysis / Continuum mechanics |
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| Outline of Final Research Achievements |
The purpose of the research plan is the development of mathematical theories to investigate the emergence of instabilities and defects at very small scales in classes of materials relevant for technological applications, such as, Shape-Memory Alloys and soft crystalline biopolymers. Regarding soft polymers, I have accomplished the full analysis of Nematic Elastomers in the elastic-foundation geometry (a configuration relevant for sensors and actuators) clarifying all the possible energy and order states. In metallurgy-related problems, on one hand, I have introduced continuum and atomistic models for describing formation of topological defects in the lattice of elastic crystals based on the variational principle and computed exact solutions for non-linear models under special symmetry assumptions. On the other hand, I have introduced probabilistic models to study martensitic transformations as a fragmentation process and found power law behavior which is in agreement with experiments.
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| Academic Significance and Societal Importance of the Research Achievements |
The modeling work has bridged across analysis (disclinations described as solutions to differential inclusions) and probability (description of self-similarity via branching random walks). This mathematical work has complemented the experimental work performed in Japanese laboratories.
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Report
(4 results)
Research Products
(30 results)
