Mathematical analysis of nonlinear elasticity for elucidation of fracture phenomena

用于阐明断裂现象的非线性弹性数学分析

• 批准号: 21740091
• 负责人: ITOU Hiromichi
• 金额: $ 1.41万
• 依托单位: Gunma University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740091/
• 关键词: 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; 線形弾性体方程式

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.

考虑到断裂现象的应用，我们研究了下列非线性问题的数学分析，并得到了结果。首先，在具有裂纹且应力应变关系服从幂律的非线性弹性力学中，我们证明了边值问题弱解的唯一可解性。其次，我们证明了在非线性条件（库仑摩擦定律和非穿透条件）下，两个粘结的不同的线性弹性介质之间的界面裂纹模型的边值问题的解的可解性。进一步研究了裂纹尖端附近解的行为。

项目成果

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On reconstruction of polygonal cavities in an elastic body with one measurement

弹性体多边形空腔的一次测量重构

• 发表时间: 2009
• 期刊: Hokkaido University Technical Report Series in Mathematics Vol.141
• 作者: Masaru Ikehata;Hiromichi Itou
• 通讯作者: Hiromichi Itou

On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement

一次测量重建线性弹性未知多边形空腔

• 发表时间: 2011
• 期刊: Journal of Physics : Conference Series
• 作者: Masaru Ikehata;Hiromichi Itou
• 通讯作者: Hiromichi Itou

Applications of Reproducing Kernels to Linear Singular Integral Equations through the Tikhonov Regularization

通过吉洪诺夫正则化再现核在线性奇异积分方程中的应用

• 发表时间: 2009
• 期刊: More Progresses in Analysis : Proceedings of the 5th International ISAAC Congress
• 作者: H.Itou;S.Saitoh
• 通讯作者: S.Saitoh

THE INTERFACE CRACK WITH COULOMB FRICTION BETWEEN TWO BONDED DISSIMILAR ELASTIC MEDIA

• DOI: 10.1007/s10492-011-0010-7
• 发表时间: 2011-02-01
• 期刊: APPLICATIONS OF MATHEMATICS
• 影响因子: 0.7
• 作者: Itou, Hiromichi;Kovtunenko, Victor A.;Tani, Atusi
• 通讯作者: Tani, Atusi