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Mathematical analysis of nonlinear elasticity for elucidation of fracture phenomena

Research Project

Project/Area Number 21740091
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionGunma University

Principal Investigator

ITOU Hiromichi  Gunma University, 大学院・工学研究科, 助教 (30400790)

Project Period (FY) 2009 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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 / 線形弾性体方程式
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.

Report

(3 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • Research Products

    (33 results)

All 2011 2010 2009 Other

All Journal Article (8 results) (of which Peer Reviewed: 6 results) Presentation (22 results) Remarks (3 results)

  • [Journal Article] The interface crack with Coulomb friction between two bonded dissimilar elastic media2011

    • Author(s)
      Hiromichi Itou、Victor A.Kovtunenko、Atusi Tani
    • Journal Title

      Applications of Mathematics Vol.56、No.1

      Pages: 69-97

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement2011

    • Author(s)
      Masaru Ikehata, Hiromichi Itou
    • Journal Title

      Journal of Physics : Conference Series

      Volume: (掲載確定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The interface crack with Coulomb friction between two bonded dissimilar elastic media2011

    • Author(s)
      Hiromichi Itou, Victor A.Kovtunenko, Atusi Tani
    • Journal Title

      Applications of Mathematics

      Volume: 56 Pages: 69-97

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The interface crack with Coulomb friction between two bonded dissimilar elastic media2010

    • Author(s)
      H.Itou, V.A.Kovtunenko, A.Tani
    • Journal Title

      Research Report, Keio University

      Volume: KSTS/RR-10/001

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Extracting the support function of acavity in an isotropic elastic body from a single set of boundary data2009

    • Author(s)
      Masaru Ikehata、Hiromichi Itou
    • Journal Title

      Inverse Problems Vol.25、No.10

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Extracting the support function of a cavity in an isotropic elastic body from a single set of boundary data2009

    • Author(s)
      Masaru Ikehata, Hiromichi Itou
    • Journal Title

      Inverse Problems Vol.25

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Applications of Reproducing Kernels to Linear Singular Integral Equations through the Tikhonov Regularization2009

    • Author(s)
      H.Itou, S.Saitoh
    • Journal Title

      More Progresses in Analysis : Proceedings of the 5th International ISAAC Congress

      Pages: 135-142

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On reconstruction of polygonal cavities in an elastic body with one measurement2009

    • Author(s)
      Masaru Ikehata, Hiromichi Itou
    • Journal Title

      Hokkaido University Technical Report Series in Mathematics Vol.141

      Pages: 44-52

    • Related Report
      2009 Annual Research Report
  • [Presentation] On Reconstruction of an Unknown Polygonal Cavity in a Linearized Elasticity with One Measurement2010

    • Author(s)
      Hiromichi Itou
    • Organizer
      International Conference on Inverse Problems (ICIP2010)
    • Place of Presentation
      City University of Hong Kong(香港、中華人民共和国)
    • Year and Date
      2010-12-16
    • Related Report
      2010 Final Research Report
  • [Presentation] On Reconstruction of an Unknown Polygonal Cavity in a Linearized Elasticity with One Measurement2010

    • Author(s)
      Hiromichi Ttou
    • Organizer
      International Conference on Inverse Problems(ICIP2010)
    • Place of Presentation
      City University of Hong Kong(Hong Kong)
    • Year and Date
      2010-12-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] On a frictional interface crack problem between dissimilar linearized elastic media2010

    • Author(s)
      Hiromichi Itou
    • Organizer
      International Conference on Applied Mathematics and Informatics (ICAMI2010)
    • Place of Presentation
      Hotel Sol Caribe San Andres(サンアンドレ、コロンビア共和国)
    • Year and Date
      2010-12-02
    • Related Report
      2010 Final Research Report
  • [Presentation] On a frictional interface crack problem between dissimilar linearized elastic media2010

    • Author(s)
      Hiromichi Itou
    • Organizer
      International Conference on Applied Mathematics and Informatics(ICAMI2010)
    • Place of Presentation
      Hotel Sol Caribe San Andres(San Andres Island, Colombia)
    • Year and Date
      2010-12-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] On a frictional interface crack problem between dissimilar linearized elastic media2010

    • Author(s)
      Hiromichi Itou
    • Organizer
      Perambulation of continuum mechanics (Meeting In Celebration of The Sixtieth Birthday of K.R.Rajagopal)
    • Place of Presentation
      Texas A&M University(テキサス州カレッジステーション、アメリカ合衆国)
    • Year and Date
      2010-11-11
    • Related Report
      2010 Final Research Report
  • [Presentation] On a frictional interface crack problem between dissimilar linearized elastic media2010

    • Author(s)
      Hiromichi Itou
    • Organizer
      Perambulation of continuum mechanics(Meeting In Celebration of The Sixtieth Birthday of K.R.Rajagopal)
    • Place of Presentation
      Texas A&M University(College station, U.S.)
    • Year and Date
      2010-11-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] On a frictional interface crack problem in dissimilar linearized elastic materials2010

    • Author(s)
      伊藤弘道、V.A.Kovtunenko、谷温之
    • Organizer
      日本数学会2010年度秋季総合分科会
    • Place of Presentation
      名古屋大学(愛知県)
    • Year and Date
      2010-09-25
    • Related Report
      2010 Final Research Report
  • [Presentation] On a frictional interface crack problem in dissimilar linearized Blastic materials2010

    • Author(s)
      伊藤弘道, V.A.Kovtunenko, 谷温之
    • Organizer
      日本数学会2010年度秋季総合分科会
    • Place of Presentation
      名古屋大学(愛知県)
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] On a frictional interface crack problem between dissimilar linearized elastic media2010

    • Author(s)
      伊藤弘道、V.A.Kovtunenko、谷温之
    • Organizer
      日本応用数理学会2010年度年会
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2010-09-09
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Coulomb摩擦と非貫通条件を考慮した異種線形弾性体界面上のき裂問題について2010

    • Author(s)
      伊藤弘道
    • Organizer
      非線形解析セミナー
    • Place of Presentation
      慶應義塾大学(神奈川県)
    • Year and Date
      2010-06-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] On reconstruction of an unknown polygonal cavity in a linearized elastic body with one measurement2010

    • Author(s)
      Hiromichi Itou
    • Organizer
      5th International Conference IP : M&S (Inverse Problems : Modeling and Simulation)
    • Place of Presentation
      Conference Center of the South Kensington campus of Lykia World & Links Golf Antalya hotel(アンタルヤ、トルコ共和国)
    • Year and Date
      2010-05-28
    • Related Report
      2010 Final Research Report
  • [Presentation] On reconstruction of an unknown polygonal cavity in a linearized elastic body with one measurement2010

    • Author(s)
      Hiromichi Itou
    • Organizer
      5th International Conference IP : M&S(Inverse Problems : Modeling and Simulation)
    • Place of Presentation
      Conference Center of the South Kensington campus of Lykia World & Links Golf Antalya hotel(Antalya, Turkey)
    • Year and Date
      2010-05-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Singularities of solutions of the linearized elasticity system near a corner or a crack tip and inverse problems2009

    • Author(s)
      伊藤弘道
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      東京大学(東京都)
    • Year and Date
      2009-12-19
    • Related Report
      2010 Final Research Report
  • [Presentation] Singularities of solutions of the linearized elasticity system near a corner or a crack tip and inverse problems2009

    • Author(s)
      Hiromichi Itou
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      東京大学
    • Year and Date
      2009-12-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] き裂先端や角における線形弾性体方程式の解の特異性と逆問題2009

    • Author(s)
      伊藤弘道
    • Organizer
      9th Workshop on Continuum Mechanics Focusing on Singularities(CoMFoS09)
    • Place of Presentation
      湘南国際村センター(神奈川県)
    • Year and Date
      2009-11-21
    • Related Report
      2010 Final Research Report
  • [Presentation] き裂先端や角における線形弾性体方程式の解の特異性と逆問題2009

    • Author(s)
      Hiromichi Itou
    • Organizer
      9th Workshop on Continuum Mechanics Focusing on Singularities(CoMFoS09)
    • Place of Presentation
      湘南国際村センター
    • Year and Date
      2009-11-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] 線形弾性体における多角形空洞の一組の観測データによる再構成について2009

    • Author(s)
      伊藤弘道、池畠優
    • Organizer
      日本応用数理学会2009年度年会
    • Place of Presentation
      大阪大学(大阪府)
    • Year and Date
      2009-09-28
    • Related Report
      2010 Final Research Report
  • [Presentation] 線形弾性体における多角形空洞の一組の観測データによる再構成について2009

    • Author(s)
      Masaru Ikehata, Hiromichi Itou
    • Organizer
      日本応用数理学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] 線形弾性体における多角形空洞の一組の観測データによる再構成について2009

    • Author(s)
      伊藤弘道
    • Organizer
      第五回非線型の諸問題
    • Place of Presentation
      長崎商工会議所(長崎県)
    • Year and Date
      2009-09-17
    • Related Report
      2010 Final Research Report
  • [Presentation] 線形弾性体における多角形空洞の一組の観測データによる再構成について2009

    • Author(s)
      Hiromichi Itou
    • Organizer
      第五回 非線型の諸問題
    • Place of Presentation
      長崎商工会議所
    • Year and Date
      2009-09-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] On reconstruction of polygonal cavities in an elastic body with one measurement2009

    • Author(s)
      Hiromichi Itou
    • Organizer
      The 34th Sapporo Symposium on Partial Differential Equations
    • Place of Presentation
      北海道大学(北海道)
    • Year and Date
      2009-08-25
    • Related Report
      2010 Final Research Report
  • [Presentation] On reconstruction of polygonal cavities in an elastic body with one measurement2009

    • Author(s)
      Hiromichi Itou
    • Organizer
      The 34th Sapporo Symposium on Partial Differential Equations
    • Place of Presentation
      北海道大学
    • Year and Date
      2009-08-25
    • Related Report
      2009 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://math.dept.eng.gunma-u.ac.jp/~h-itou/

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://math.dept.eng.gunma-u.ac.jp/~h-itou/

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://math.dept.eng.gunma-u.ac.jp/~h-itou/

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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