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Numerical crack path selection problem based on energy profiles

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Abstract

Given the infinite number of possible crack paths in a material, a mathematical theory to determine a crack path has not yet been established. On this occasion, we numerically find a crack path in a variational fracture framework. Based on the variational crack propagation model by Francfort and Marigo, we numerically compare elastic energy profiles along several crack paths and determine a crack path with a minimum energy profile. We consider multiple straight crack cases and kink- and circle-shaped crack paths. For these cases, we additionally employ a variational formula for the derivative of the energy profile. Furthermore, we numerically observe that our approach’s selected kink crack path exhibits good agreement with the crack propagation results in the phase field model.

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Acknowledgements

This research was supported/partially supported by the Ministry of Education, Culture, Sports, Science, and Technology-Japan (MEXT) Scholarship and JSPS KAKENHI (Grant numbers JP20H01812 and JP20KK0058).

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Author notes

  1. Sayahdin Alfat

    Present address: Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa, 920-1192, Japan

Authors and Affiliations

  1. Kanazawa University, Kakuma, Kanazawa, 920-1192, Japan

    Mahardhika Maulana Alifian

  2. Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa, 920-1192, Japan

    Mahardhika Maulana Alifian

  3. Faculty of Mathematics and Physics, Kanazawa University, Kakuma, Kanazawa, 920-1192, Japan

    Masato Kimura

  4. Physics Education Department, Halu Oleo University, Kendari, Southeast Sulawesi, Indonesia

    Sayahdin Alfat

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  1. Mahardhika Maulana Alifian
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  2. Masato Kimura
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Correspondence to Mahardhika Maulana Alifian.

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Alifian, M.M., Kimura, M. & Alfat, S. Numerical crack path selection problem based on energy profiles. Japan J. Indust. Appl. Math. 39, 817–841 (2022). https://doi.org/10.1007/s13160-022-00523-0

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  • DOI: https://doi.org/10.1007/s13160-022-00523-0

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