A Phase Field Approach to Mathematical Modeling of Crack Propagation

  • Masato Kimura
  • Takeshi Takaishi
Part of the Mathematics for Industry book series (MFI, volume 5)


We consider a phase field model for crack propagation in an elastic body. The model is derived as an irreversible gradient flow of the Francfort-Marigo energy with the Ambrosio-Tortorelli regularization and is consistent to the classical Griffith theory. Some numerical examples computed by adaptive mesh finite element method are presented.


Adaptive mesh finite element method Crack propagation Fracture mechanics Irreversible system Phase field model 



This work was partially supported by JSPS KAKENHI Grant Number 00268666.


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Science and EngineeringKanazawa UniversityKakuma, KanazawaJapan
  2. 2.Faculty of Information DesignHiroshima Kokusai Gakuin UniversityHiroshimaJapan

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