Friction Versus Damage: Dynamic Self-similar Crack Growth Revisited

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


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.



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


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.College of Science and EngineeringRitsumeikan UniversityKusatsu, ShigaJapan

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