2017 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 |
One published paper and one submitted paper (currently under review).
Completed the analysis and modeling of nematic elastomer foundations (thin elastic membranes made of a soft shape-memory composite material) by Gamma-convergence. Discovered mechanism for tuning the elastic properties of the composite by actuation on the optical microstructure. A joint paper with Dr. Andres A. L. Baldelli (CNRS, Paris) has been submitted for publication and is available online at https://arxiv.org/abs/1711.08692 . Initiated the numerical modeling of experiments of nematic elastomer membranes in a configuration similar to the one analyzed theoretically.
Completed the analysis of a reaction-diffusion Allen-Cahn-Hilliard model. Computed the exact solutions in some relevant geometrical regimes. Joint work with the group of P Broadbridge, D. Triadis and D. Gallage (PhD student, in co-supervision with La Trobe University). A joint paper has been published on Symmetry.
Stochastic modeling of martensitic microstructure and avalanches. Paper on 2-, 3-D analysis of a fragmentation process describing martensitic microstructure will be submitted shortly (joint work with Ben Hambly, Oxford). Initiated new work on alternative models based on fragmentation and branching.
Initiated analytical work on disclinations in metal alloys according to an atomistic model. Collaboration with Patrick van Meurs (Kanazawa).
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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
All on schedule.
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| Strategy for Future Research Activity |
1) Nematic elastomer membranes. I will continue work on the numerical modeling of nematic elastomer foundations based on the finite element method (in collaboration with Andres A. L. Baldelli). If possible, I will liaise with the experimental group of Prof. Francesco Greco (Graz Institute of Technology) with the aim of nematic foundations in modeling experimental which are relevant for applications in electronics.
2) Stochastic modeling of martensite microstructure and avalanches. I will continue the work on fragmentation models for describing martensitic microstructure and avalanches with the goal of incorporating new effects, possibly branching and hysteresis. If possible, I will compare analytical findings with the experiments on avalanches and disclinations from the group of Prof. Tomonari Inamura (Tokyotech).
3) Atomistic modeling of disclinations. I will continue the modeling work on disclinations in elastic media initiated with Dr. Patrick van Meurs. Our main goal is to derive a variational model via passage from atomistic to continuum description of topological defects in a 2D triangular lattice. Once analytical data is obtained, perform numerical analysis to test the model.
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| Causes of Carryover |
I will use in the following year for extended visits at the Mathematical Institute in Oxford and at the University of Cambridge.
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