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Friction Versus Damage: Dynamic Self-similar Crack Growth Revisited

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Mathematical Analysis of Continuum Mechanics and Industrial Applications III (CoMFoS 2018)

Part of the book series: Mathematics for Industry ((MFI,volume 34))

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Abstract

Seismological observational studies have revealed that earthquakes exhibit dynamic self-similar crack growth constituting 50–90% of the shear wave velocity. Remarkably, the peak slip velocity defined on the crack surface is scale-invariant, even from M1 to M9 earthquakes. However, a classical self-similar crack model with a singularity does not satisfy all the observed properties above. In this chapter, we review these discrepancies and introduce friction and damage models to solve them, which have been proposed in several numerical studies. We show that velocity-dependent friction can fulfill some requirements of the observations, while slip- or time-dependent friction cannot. We finally discuss the theoretical equivalence of friction and damage model for a self-similar crack in terms of energetics, which has previously only been implied by numerical studies.

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Acknowledgments

This work was supported by JSPS KAKENHI Grant No. 17H02857.

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Authors and Affiliations

  1. College of Science and Engineering, Ritsumeikan University, 1-1-1, Noji Higashi, Kusatsu, Shiga, 525-8577, Japan

    Shiro Hirano

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  1. Shiro Hirano
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Correspondence to Shiro Hirano .

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Editors and Affiliations

  1. Department of Mathematics, Tokyo University of Science, Tokyo, Japan

    Hiromichi Itou

  2. College of Science and Engineering, Ritsumeikan University, Kusatsu, Japan

    Shiro Hirano

  3. Faculty of Mathematics and Physics, Kanazawa University, Kanazawa, Ishikawa, Japan

    Masato Kimura

  4. NAWI Graz, Institut für Mathematik, Karl-Franzens University of Graz, Graz, Austria

    Victor A. Kovtunenko

  5. Siberian Branch of RAS, Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia

    Alexandr M. Khludnev

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Hirano, S. (2020). Friction Versus Damage: Dynamic Self-similar Crack Growth Revisited. In: Itou, H., Hirano, S., Kimura, M., Kovtunenko, V.A., Khludnev, A.M. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications III. CoMFoS 2018. Mathematics for Industry, vol 34. Springer, Singapore. https://doi.org/10.1007/978-981-15-6062-0_12

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