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Theoretical and numerical analysis for a phase-field model describing the crack growth phenomenon

Research Project

Project/Area Number 19K14605
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionHokkaido University (2021-2023)
National Institute of Advanced Industrial Science and Technology (2019-2020)

Principal Investigator

Gao Yueyuan  北海道大学, 電子科学研究所, 特任助教 (80807793)

Project Period (FY) 2019-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
KeywordsCrack growth phenomenon / Fracture toughness / Phase-field models / J-integral / Inverse problem / Numerical analysis / Inhomogeneity / Inverse problem / Phase-field Model / Inverse estimation / Data science / Phase-field model / Finite volume method
Outline of Research at the Start

The research of this project is based on the phase-field model by Takaishi and Kimura which describes the crack growth phenomenon in materials science. The model is a partial differential equations system involving the positive-part function. We study the connection between the structure of the material in deterministic and stochastic cases and the toughness of the material. We perform numerical simulations by finite volume methods and investigate the well-posedness of the system by means of the convergence of the numerical scheme.

Outline of Final Research Achievements

We study the crack propagation in an inhomogeneous media in which fracture toughness varies in space. Using the two phase-field models based on two different surface energy functionals, which are so called AT1 and AT2 models, we perform simulations of the crack propagation by finite volume method and show that the J-integral reflects the effective in-homogeneous toughness. Then, we formulate inverse problems to estimate space-dependent fracture toughness from the crack path. Our method, which is based on data pre-processing and regression, successfully estimates the positions and magnitude of tougher regions for different geometry of inhomogeneity. And we compare the advantages and disadvantages of the AT1 and AT2 models.

Academic Significance and Societal Importance of the Research Achievements

き裂の進展現象は破壊力学の重要な課題である。勾配流型のフェーズフィールドモデルは、き裂の進展現象を理論的に理解する道具として重要なモデルとなっている。き裂の進展現象の理論解析を行うためには、異なるフェーズフィルドモデルの解析と逆問題への活用が必須である。この研究では、き裂の進展を記述するフェーズフィルドモデルに注目して、き裂進展現象のシミュレーションと均一や不均一材料の破壊靭性値の推定を行い、その解析から二つ異なった表面エネルギーから得られたフェーズフィルドモデル特徴の解明を行った。

Report

(6 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (12 results)

All 2023 2022 2021 2020 2019

All Journal Article (3 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 3 results,  Open Access: 3 results) Presentation (9 results) (of which Int'l Joint Research: 1 results)

  • [Journal Article] Inverse problems of inhomogeneous fracture toughness using phase-field models2023

    • Author(s)
      Gao Yueyuan、Yoshinaga Natsuhiko
    • Journal Title

      Physica D: Nonlinear Phenomena

      Volume: 448 Pages: 133734-133734

    • DOI

      10.1016/j.physd.2023.133734

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Generalized Finite Volume Method for Density Driven Flows in Porous Media2021

    • Author(s)
      Gao Yueyuan、Hilhorst Danielle、Vu Do Huy Cuong
    • Journal Title

      Energies

      Volume: 14 Issue: 19 Pages: 6151-6151

    • DOI

      10.3390/en14196151

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Existence and uniqueness of the entropy solution of a stochastic conservation law with a Q‐Brownian motion2020

    • Author(s)
      Funaki Tadahisa、Gao Yueyuan、Hilhorst Danielle
    • Journal Title

      Mathematical Methods in the Applied Sciences

      Volume: 43 Issue: 9 Pages: 5860-5886

    • DOI

      10.1002/mma.6329

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] フェーズフィールドモデルを用いた不均一材料の破壊靭性値の推定2023

    • Author(s)
      Gao Yueyuan, 義永 那津人
    • Organizer
      令和5年度 日本数学会 中国・四国支部例会
    • Related Report
      2023 Annual Research Report
  • [Presentation] Inverse estimation of inhomogeneous materials’ fracture toughness by using a phase-field model2022

    • Author(s)
      Gao Yueyuan, 義永那津人
    • Organizer
      第27回計算工学講演会
    • Related Report
      2022 Research-status Report
  • [Presentation] Numerical simulations of PDE models in material science2021

    • Author(s)
      Gao Yueyuan
    • Organizer
      第 15 回応用数理研究会
    • Related Report
      2021 Research-status Report
  • [Presentation] Inverse estimation of inhomogeneous materials' fracture toughness by using a phase-field model2021

    • Author(s)
      Gao Yueyuan, 義永那津人
    • Organizer
      2021年度応用数学合同研究集会 、【解析系セッション】
    • Related Report
      2021 Research-status Report
  • [Presentation] フェーズフィールドモデルを用いた不均一材料の破壊靭性値の推定2021

    • Author(s)
      Gao Yueyuan
    • Organizer
      北陸応用数理研究会2022
    • Related Report
      2021 Research-status Report
  • [Presentation] Numerical simulations of a PDE model for crack growth phenomenon2021

    • Author(s)
      Gao Yueyuan, Yoshinaga Natsuhiko
    • Organizer
      第7回 北大・部局横断シンポジウム ポスターセッション
    • Related Report
      2021 Research-status Report
  • [Presentation] Numerical Study of a PDE Model for Crack Growth Phenomenon2021

    • Author(s)
      Gao Yueyuan, Yoshinaga Natsuhiko
    • Organizer
      The 22nd RIES-Hokudai International symposium, [癒] ポスターセッション
    • Related Report
      2021 Research-status Report
  • [Presentation] A generalized finite volume method for density driven flows in porous media2020

    • Author(s)
      Yueyuan Gao
    • Organizer
      12th Annual InterPore Meeting (IntePore2020)
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Uniqueness of the Entropy Solution of a Stochastic Conservation Law with a Q-Brownian Motion2019

    • Author(s)
      Yueyuan Gao
    • Organizer
      The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI); Stochastic Analysis, Random Fields and Integrable Probability
    • Related Report
      2019 Research-status Report

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Published: 2019-04-18   Modified: 2025-01-30  

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