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Study of crack propagation models and moving boundary problems

Research Project

Project/Area Number 21540136
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKyushu University

Principal Investigator

KIMURA Masato  九州大学, マス・フォア・インダストリ研究所, 准教授 (70263358)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords亀裂進展モデル / 移動境界問題 / フェーズフィールドモデル / 多角形版移動境界問題 / ヘレショウ移動境界問題 / 粒子法 / 打ち切り誤差 / エネルギー解放率 / 亀裂進展 / 反応拡散系 / 特異摂動問題 / 固有値問題 / 面積保存
Research Abstract

In this research, we studied several crack propagation models in fracture mechanics and related various moving boundary problems from viewpoints of mathematical and numerical analyses. These are completely different phenomena, however, both have geometrical difficulty and importance of variational structures. We succeeded in proposing a phase field model by means of reaction diffusion system, which is a powerful tool in moving boundary problems, and constructed a polygonal motion with variational structure and its numerical analysis.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (41 results)

All 2012 2011 2010 2009

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (27 results)

  • [Journal Article] Differentiability of potential energies with a parameter and shape sensitivity analysis for nonlinear case2012

    • Author(s)
      K. Ohtsuka and M. Kimura
    • Journal Title

      the p-Poisson problem, Japan J. Indust. Appl

      Volume: Vol.29, No.1 Pages: 23-35

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Differentiability of potential energies with a parameter and shape sensitivity analysis for nonlinear case : the p-Poisson problem2012

    • Author(s)
      K.Ohtsuka, M.Kimura
    • Journal Title

      Japan J.Indust.Appl.Math.

      Volume: Vol.29, No.1 Pages: 23-35

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computational studies of non-local anisotropic Allen-Cahn equation2011

    • Author(s)
      M. Benes, S. Yazaki and M. Kimura
    • Journal Title

      Math. Bohem

      Volume: Vol.136, No.4 Pages: 429-437

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Shape derivative of potential energy and energy release rate in fracture mechanics2011

    • Author(s)
      M. Kimura and I. Wakano
    • Journal Title

      Journal of Math-for-industry

      Volume: Vol.3 Pages: 21-31

    • NAID

      40019161196

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Phase field models for crack propagation2011

    • Author(s)
      M. Kimura and T. Takaishi
    • Journal Title

      Theoretical and Applied Mechanics Japan

      Volume: Vol.59 Pages: 85-90

    • NAID

      130004463793

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Shape derivative of potential energy and energy release rate in fracture mechanics2011

    • Author(s)
      M.Kimura, I.Wakano
    • Journal Title

      Journal of Math-for-industry

      Volume: Vol.3A Pages: 21-31

    • NAID

      40019161196

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computational studies of non-local anisotropic Allen-Cahn equation2011

    • Author(s)
      M.Benes, S.Yazaki, M.Kimura
    • Journal Title

      Math.Bohem.

      Volume: Vol.136, No.4 Pages: 429-437

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] メッシュフリー粒子法における差分公式の打ち切り誤差解析2010

    • Author(s)
      石島清宏, 木村正人
    • Journal Title

      日本応用数理学会論文誌

      Volume: Vol.20, No.3 Pages: 165-182

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Second order numerical scheme for motion of polygonal curves with constant area speed2009

    • Author(s)
      M. Benes, M. Kimura and S. Yazaki
    • Journal Title

      Interfaces and Free Boundaries

      Volume: vol.11, no.4 Pages: 515-536

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type2009

    • Author(s)
      S. Jimbo, M. Kimura and H. Notsu
    • Journal Title

      Asymtotic Analysis

      Volume: vol.65 Pages: 103-123

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Phase field model for mode III crack growth in two dimensional elasticity2009

    • Author(s)
      T. Takaishi and M. Kimura
    • Journal Title

      Kybernetika

      Volume: vol.45, no.4 Pages: 605-614

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Phase field model for mode III crack growth in two dimensional elasticity2009

    • Author(s)
      T.Takaishi, M.Kimura
    • Journal Title

      Kybernetika Vol.45 No.4

      Pages: 605-614

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type2009

    • Author(s)
      S.Jimbo, M.Kimura, H.Notsu
    • Journal Title

      Asymtotic Analysis Vol.65

      Pages: 103-123

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Second order numerical scheme for motion of polygonal curves with constant area speed2009

    • Author(s)
      M.Benes, M.Kimura, S.Yazaki
    • Journal Title

      Interfaces and Free Boundaries Vol.11 No.4

      Pages: 515-536

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 粒子法の勾配差分の打ち切り誤差評価と重み関数2012

    • Author(s)
      木村正人
    • Organizer
      粒子法研究会(第十六回)
    • Place of Presentation
      東京大学工学部
    • Year and Date
      2012-03-02
    • Related Report
      2011 Final Research Report
  • [Presentation] エネルギー勾配構造をもつ振動・破壊モデル2011

    • Author(s)
      木村正人
    • Organizer
      中木記念シンポジウム
    • Place of Presentation
      広島大学東千田キャンパス
    • Year and Date
      2011-12-07
    • Related Report
      2011 Final Research Report
  • [Presentation] エネルギー変分型の破壊現象モデル2011

    • Author(s)
      木村正人
    • Organizer
      ウィンタースクール数理モデルの産業・諸科学への活用-数理モデルの夢
    • Place of Presentation
      富士通汐留シティセンター
    • Year and Date
      2011-12-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Gradient flow models in elasticity-crack and dislocation dynamics2011

    • Author(s)
      Masato Kimura
    • Organizer
      Workshop on Reliability in Scientific Computing and Related Topics
    • Place of Presentation
      Saikai National Park Kujyukushima Visitor Center, Sasebo JAPAN
    • Year and Date
      2011-11-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Gradient flow models in elasticity---crack and dislocation dynamics2011

    • Author(s)
      Masato Kimura
    • Organizer
      Workshop on Reliability in Scientific Computing and Related Topics
    • Place of Presentation
      Saikai National Park Kujyukushima Visitor Center, Sasebo JAPAN
    • Year and Date
      2011-11-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] 亀裂進展および転位運動のエネルギー勾配流モデル2011

    • Author(s)
      木村正人
    • Organizer
      第11回盛岡応用数学小研究集会
    • Place of Presentation
      岩手大学
    • Year and Date
      2011-11-12
    • Related Report
      2011 Final Research Report
  • [Presentation] Continuous and discretecrack propagation models with energy gradient property2011

    • Author(s)
      Masato Kimura
    • Organizer
      Forum Math-for-Industry
    • Place of Presentation
      University of Hawai' i
    • Year and Date
      2011-10-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Continuous and discretecrack propagation models with energy gradient property2011

    • Author(s)
      Masato Kimura
    • Organizer
      Forum "Math-for-Industry" 2011 (FMI2011)
    • Place of Presentation
      University of Hawai'i
    • Year and Date
      2011-10-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] Energy gradient systems in fracture and dislocation dynamics2011

    • Author(s)
      Masato Kimura
    • Organizer
      CASA Colloquium
    • Place of Presentation
      Eindhoven University of Technology
    • Year and Date
      2011-09-07
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Truncation error analysis for particle methods, EASIAM20112011

    • Author(s)
      Masato Kimura
    • Place of Presentation
      Waseda University, Kitakyushu Campus
    • Year and Date
      2011-06-28
    • Related Report
      2011 Final Research Report
  • [Presentation] Truncation error analysis for particle methods2011

    • Author(s)
      Masato Kimura
    • Organizer
      EASIAM2011
    • Place of Presentation
      Waseda University, Kitakyushu Campus
    • Year and Date
      2011-06-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] 転位線運動のフェーズフィールドモデルとPeach-Koehler力2011

    • Author(s)
      木村正人
    • Organizer
      日本応用数理学会 2011年研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都)
    • Year and Date
      2011-03-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] 転位線運動のフェーズフィールドモデルとPeach-Koehler力2011

    • Author(s)
      木村正人
    • Organizer
      日本応用数理学会2011年研究部会連合発表会
    • Place of Presentation
      電気通信大学
    • Related Report
      2011 Final Research Report
  • [Presentation] 弾性体のバネ質点系近似についての考察2011

    • Author(s)
      木村正人
    • Organizer
      ワークショップ連続体力学の現象と数理
    • Place of Presentation
      九州大学西新プラザ
    • Related Report
      2011 Final Research Report
  • [Presentation] Parameter variation theorems and applications to crack problems2011

    • Author(s)
      木村正人
    • Organizer
      第28回九州における偏微分方程式研究集会
    • Place of Presentation
      九州大学西新プラザ
    • Related Report
      2011 Final Research Report
  • [Presentation] On some generalizations of polygonal motions2010

    • Author(s)
      Masato Kimura
    • Organizer
      Czech-Japanese Seminar in Applied Mathematics 2010
    • Place of Presentation
      チェコ工科大学(プラハ,チェコ共和国)
    • Year and Date
      2010-09-01
    • Related Report
      2010 Annual Research Report
  • [Presentation] 亀裂進展現象を記述するフェーズフィールドモデルについて2010

    • Author(s)
      木村正人
    • Organizer
      第59回理論応用力学講演会
    • Place of Presentation
      日本学術会議(東京都)
    • Year and Date
      2010-06-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] 変分構造を持つ多角形移動境界問題2010

    • Author(s)
      木村正人
    • Organizer
      10th Workshop of CoMFoS
    • Place of Presentation
      岡山理科大学
    • Related Report
      2011 Final Research Report
  • [Presentation] 多角形運動における多角形曲率の一般化とその応用2010

    • Author(s)
      木村正人
    • Organizer
      数値解析と計算の信頼性評価
    • Place of Presentation
      ハウステンボス,佐世保
    • Related Report
      2011 Final Research Report
  • [Presentation] 多角形曲率の一般化と移動境界問題への応用2010

    • Author(s)
      木村正人
    • Organizer
      科学技術計算アルゴリズムの数理的基盤と展開
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Final Research Report
  • [Presentation] On some generalizations of polygonal motions2010

    • Author(s)
      Masato Kimura
    • Organizer
      Czech-Japanese Seminar in Applied Mathematics
    • Place of Presentation
      Czech Technical University, Czech Republic
    • Related Report
      2011 Final Research Report
  • [Presentation] On some generalizations of polygonal motions, Tutorial Lectures and International Workshop2010

    • Author(s)
      Masato Kimura
    • Organizer
      Singular Diffusion and Evolving Interfaces
    • Place of Presentation
      Hokkaido University, Japan
    • Related Report
      2011 Final Research Report
  • [Presentation] 亀裂進展現象を記述するフェーズフィールドモデルについて2010

    • Author(s)
      木村正人
    • Organizer
      第59回理論応用力学講演会(NCTAM2010)
    • Place of Presentation
      日本学術会議
    • Related Report
      2011 Final Research Report
  • [Presentation] 楕円型エネルギーの領域変分に対するパラメータ変分公式の応用2010

    • Author(s)
      木村正人
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶應義塾大学
    • Related Report
      2011 Final Research Report
  • [Presentation] バナッハ空間におけるパラメータ変分公式と亀裂問題におけるエネルギー解放率2010

    • Author(s)
      木村正人
    • Organizer
      ワークショップ変分法と領域摂動
    • Place of Presentation
      神戸インスティチュート
    • Related Report
      2011 Final Research Report
  • [Presentation] 線形および非線形楕円型エネルギーの領域変分2009

    • Author(s)
      木村正人
    • Organizer
      2009年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学
    • Related Report
      2011 Final Research Report
  • [Presentation] フェイズ・フィールドを用いたモードIII亀裂進展の数理モデルとシミュレーション2009

    • Author(s)
      木村正人
    • Organizer
      産業技術数理研究センター第7回ワークショップ,水素利用社会の実現に向けた数値解析からの貢献
    • Place of Presentation
      九州大学
    • Related Report
      2011 Final Research Report

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

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