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International Journal of Fracture

, Volume 204, Issue 2, pp 225–237 | Cite as

A fiber-bundle model for the continuum deformation of brittle material

  • K. Z. Nanjo
Original Paper
  • 282 Downloads

Abstract

The deformation of brittle material is primarily accompanied by micro-cracking and faulting. However, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. To explain this rheology, we use a fiber-bundle model, which is a model of damage mechanics. In our analyses, yield stress was introduced. Above this stress, we hypothesize that the fibers begin to fail and a failed fiber is replaced by a new fiber. This replacement is analogous to a micro-crack or an earthquake and its iteration is analogous to stick–slip motion. Below the yield stress, we assume that no fiber failure occurs, and the material behaves elastically. We show that deformation above yield stress under a constant strain rate for a sufficient amount of time can be modeled as an equation similar to that used for non-Newtonian viscous flow. We expand our rheological model to treat viscoelasticity and consider a stress relaxation problem. The solution can be used to understand aftershock temporal decay following an earthquake. Our results provide justification for the use of a non-Newtonian viscous flow to model the continuum deformation of brittle materials.

Keywords

Fracture Brittle deformation Rheology Fiber-bundle Yield stress Viscoelasticity 

Notes

Acknowledgements

The author thanks the Editor K. Ravi-Chandar and two anonymous reviewers for constructive comments. A part of this study was conducted under the auspices of the MEXT Program for Promoting the Reform of National Universities.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Global Center for Asian and Regional ResearchUniversity of ShizuokaShizuokaJapan
  2. 2.Institute of Advanced SciencesYokohama National UniversityYokohamaJapan

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