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

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K14605
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Hokkaido 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
• Keywords: Crack growth phenomenon / Fracture toughness / Phase-field models / J-integral / Inverse problem / Numerical analysis

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.

Free Research Field

応用数学

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。