2010 Fiscal Year Final Research Report
Mathematical analysis of nonlinear elasticity for elucidation of fracture phenomena
| Project/Area Number |
21740091
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Gunma University |
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Principal Investigator |
ITOU Hiromichi Gunma University, 大学院・工学研究科, 助教 (30400790)
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| Project Period (FY) |
2009 – 2010
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| Keywords | 非線形弾性体方程式 / 破壊力学 / き裂 / 逆問題 / 非破壊検査 / 摩擦 / 非貫通条件 |
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| Research Abstract |
With application to fracture phenomena in mind, we studied mathematical analyses for the following nonlinear problems and obtained the results. First, in nonlinear elasticity which has a crack and the stress-strain relation is governed by power law, we showed a unique solvability of the weak solution for the boundary value problem. Second, we proved a solvability of the solution of a boundary value problem as a model of interfacial crack under the nonlinear condition (Coulomb friction law and non-penetration condition) between two bonded dissimilar linearized elastic media. Further, we investigated the behavior of the solution near the crack tip.
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