Elucidation of fracture phenomena from the viewpoint of singularity of solutions of partial differential equations at crack tips
Project/Area Number |
23740101
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
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Research Institution | Tokyo University of Science (2013) Gunma University (2011-2012) |
Principal Investigator |
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Project Period (FY) |
2011 – 2014
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Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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Keywords | き裂 / 非線形弾性体 / 粘弾性体 / 剛性介在物 / 逆問題 / 弾性理論 / 非貫通条件 / 介在物 / 剛性率 / 剥離 / 準線形楕円型方程式 / 破壊力学 |
Outline of Final Research Achievements |
With application of fracture phenomena in mind, we studied the behavior of solutions of partial differential equations at crack tips. In a case of nonlinear equations we did not achieve anything new, but we found a toehold to solve the problem. In a case of boundary value problems in two dimensional elasticity with rigid line inclusions, we proved the existence and uniqueness of the solution and derived the convergent series expansion of the solution near the tip of the rigid inclusion. As an application of this study, we considered a reconstruction problem for cavities in three dimensional linear viscoelasticity, and we established a formula extracting three kinds of information about the unknown cavity from measured data on the boundary.
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Report
(4 results)
Research Products
(17 results)