2019 Fiscal Year Annual Research Report
Mesoscale modeling for disclinations toward a theory for kink and material strengthening
Publicly Offered Research
| Project Area | Materials science on mille-feullie structure -Developement of next-generation structural materials guided by a new strengthen principle- |
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| Project/Area Number |
19H05131
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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) |
2019-04-01 – 2021-03-31
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| Keywords | Disclinations / Kink formation / Calculus of Variations / Solid Mechanics |
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| Outline of Annual Research Achievements |
Developed an analytical theory to describe self-similar microstructures in elastic crystals as the solutions to differential inclusion problems in non-linear elasticity (1 paper). As an application, performed exact constructions of disclinations observed in lead-orthovanadate and provided energy estimates. Computed numerical solutions to compression experiments of columnar structures modelling various lattice symmetries. Showed that kinks emerge due to interplay of structural vs. material instabilities. Preliminary results complement existing literature on the kinematics of disclinations and kinks by providing a setting in the framework of minimization problems for non-convex energies (1 paper in preparation).
Computed exact solutions to a fourth order model for surface diffusion (1 paper).
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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
A first paper on the modeling of disclinations has been accepted for publication on ARMA. This paves the way to modeling of disclinations and other mismatches in single-slip plasticity models. Another paper describing surface-diffusion in metals has been published on Physica D. A paper is being prepared on the modeling of disclinations caused by angular mismatches in the crystallographic lattice by means of an atomistic nearest-neighbor-type model in planar domains. Submission expected soon. A paper describing numerical computation of kink formation in columnar structures based on a continuum model capable of describing micro-plasticity is currently in progress.
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| Strategy for Future Research Activity |
To continue the analysis of a continuum, non-convex model in non-linear elasticity capable of detecting plasticity at the lattice level. To compute solutions to compression and extension experiments in simple geometries. To compute stress-strain curves and phase-diagrams depending on geometrical and material parameters and show the effect of parameters on various morphologies of kinks. To elucidate the effects of kinks and disclinations on the overall physical properties of the material.
To continue the variational analysis of atomistic models for planar disclinations.
To initiate the modeling and analysis of disclinations with a semi-discrete (diffuse-core) approach by means of Gamma-convergence.
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