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A Phase Field Approach to Mathematical Modeling of Crack Propagation

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A Mathematical Approach to Research Problems of Science and Technology

Part of the book series: Mathematics for Industry ((MFI,volume 5))

Abstract

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.

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Acknowledgments

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

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Authors and Affiliations

  1. Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa, 920-1192, Japan

    Masato Kimura

  2. Faculty of Information Design, Hiroshima Kokusai Gakuin University, 6-20-1 Nakano, Aki-ku, Hiroshima, 739-0321, Japan

    Takeshi Takaishi

Authors
  1. Masato Kimura
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  2. Takeshi Takaishi
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Corresponding author

Correspondence to Masato Kimura .

Editor information

Editors and Affiliations

  1. Kyushu University, Fukuoka, Japan

    Ryuei Nishii

  2. Department of Mathematics, Hokkaido University, Sapporo, Japan

    Shin-ichiro Ei

  3. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Miyuki Koiso

  4. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Hiroyuki Ochiai

  5. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Kanzo Okada

  6. Faculty of Arts and Science, Kyushu University, Fukuoka, Japan

    Shingo Saito

  7. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Tomoyuki Shirai

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Kimura, M., Takaishi, T. (2014). A Phase Field Approach to Mathematical Modeling of Crack Propagation. In: Nishii, R., et al. A Mathematical Approach to Research Problems of Science and Technology. Mathematics for Industry, vol 5. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55060-0_13

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  • DOI: https://doi.org/10.1007/978-4-431-55060-0_13

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  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-55059-4

  • Online ISBN: 978-4-431-55060-0

  • eBook Packages: EngineeringEngineering (R0)

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