A damage-mechanics model for fracture nucleation and propagation

Department of Physics, Boston University, Boston, MA 02215, United States
Theoretical and Applied Fracture Mechanics (Impact Factor: 1.26). 06/2010; 53(3):180-184. DOI: 10.1016/j.tafmec.2010.06.002


In this paper, a composite model for earthquake rupture initiation and propagation is proposed. The model includes aspects of damage mechanics, fiber-bundle models, and slider-block models. An array of elements is introduced in analogy to the fibers of a fiber bundle. Time to failure for each element is specified from a Poisson distribution. The hazard rate is assumed to have a power-law dependence on stress. When an element fails it is removed, the stress on a failed element is redistributed uniformly to a specified number of neighboring elements in a given range of interaction. Damage is defined to be the fraction of elements that have failed. Time to failure and modes of rupture propagation are determined as a function of the hazard-rate exponent and the range of interaction.

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Available from: James R Holliday, Jun 04, 2014
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    • "Lee et al. (2012a, b) found negative correlation between b and the Hurst exponent values in real seismicity and their model, a Long-Range Connective Sandpile (LRCS). Other applications of CA related to seismicity include damagemechanics models for fracture (Yakovlev et al. 2010) to model the subduction phenomenon (Leduc 1997); Steacy and Sammis (1991) proposed a CA model to the formation of fractal patterns of fragmentation in fault zones, and interpreted the values found in real faults in terms of the packing configuration. CA have been used to study the Mode-I crack propagation (He and Li 2010), to study rock failure and earthquake process on mesoscopic scale (Wang et al. 2000), to model the fluid-rock interaction on volcano mechanics (Lahaie and Grasso 1998), to model wave propagation (Leamy 2008), or to model the lithosphere degassing (Iudin and Grigoriev 2003), for example. "
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    ABSTRACT: Cellular Automata have been used in the literature to describe seismicity. We first historically introduce Cellular Automata and provide some important definitions. Then we proceed to review the most important models, most of them being variations of the spring-block model proposed by Burridge and Knopoff, and describe the most important results obtained from them. We discuss the relation with criticality and also describe some models that try to reproduce real data.
    Acta Geophysica 12/2013; 61(6). DOI:10.2478/s11600-013-0144-y · 1.07 Impact Factor
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    Treatise on Geophysics, 2nd edited by G. Schubert, H. Kanamori, 04/2015: chapter Complexity and Earthquakes: pages 627-653; Elsevier.