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# A damage-mechanics model for fracture nucleation and propagation

Department of Physics, One Shields Ave., University of California, Davis, CA 95616, United States; Department of Geology, One Shields Ave., University of California, Davis, CA 95616, United States; Sante Fe Institute, Santa Fe, NM 87501, United States; Department of Physics, Boston University, Boston, MA 02215, United States

Theoretical and Applied Fracture Mechanics (Impact Factor: 0.63). 06/2010; DOI: 10.1016/j.tafmec.2010.06.002 - Citations (14)
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**ABSTRACT:**The dynamic behavior of a simple mechanical model of an earthquake fault is studied. This model, introduced originally by Burridge and Knopoff (1967), consists of an elastically coupled chain of masses in contact with a moving rough surface. The present version of the model retains the full Newtonian dynamics with inertial effects and contains no externally imposed stochasticity or spatial inhomogeneity. The only nonlinear feature is a velocity-weakening stick-slip friction force between the masses and the moving surface. This system is being driven persistently toward a slipping instability and therefore exhibits noisy sequences of earthquakelike events. These events are observed in numerical simulations, and many of their features can be predicted analytically.Physical Review A 01/1990; 40(11):6470-6484. · 3.04 Impact Factor -
##### Article: Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems

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**ABSTRACT:**1] Earthquakes and the faults upon which they occur interact over a wide range of spatial and temporal scales. In addition, many aspects of regional seismicity appear to be stochastic both in space and time. However, within this complexity, there is considerable self-organization. We argue that the occurrence of earthquakes is a prob-lem that can be attacked using the fundamentals of statistical physics. Concepts of statistical physics associ-ated with phase changes and critical points have been successfully applied to a variety of cellular automata models. Examples include sandpile models, forest fire models, and, particularly, slider block models. These models exhibit avalanche behavior very similar to ob-served seismicity. A fundamental question is whether variations in seismicity can be used to successfully fore-cast the occurrence of earthquakes. Several attempts have been made to utilize precursory seismic activation and quiescence to make earthquake forecasts, some of which show promise. INDEX TERMS:, Statistical physics approach to understanding the multi-scale dynamics of earthquake fault systems, Rev. Geophys., 41(4), 1019, doi:10.1029/2003RG000135, 2003.Reviews of Geophysics 01/2003; 41(4). · 13.91 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Fiber bundle models, where fibers have random lifetimes depending on their load histories, are useful tools in explaining time-dependent failure in heterogeneous materials. Such models shed light on diverse phenomena such as fatigue in structural materials and earthquakes in geophysical settings. Various asymptotic and approximate theories have been developed for bundles with various geometries and fiber load-sharing mechanisms, but numerical verification has been hampered by severe computational demands in larger bundles. To gain insight at large size scales, interest has returned to idealized fiber bundle models in 1D. Such simplified models typically assume either equal load sharing (ELS) among survivors, or local load sharing (LLS) where a failed fiber redistributes its load onto its two nearest flanking survivors. Such models can often be solved exactly or asymptotically in increasing bundle size, N, yet still capture the essence of failure in real materials. The present work focuses on 1D bundles under LLS. As in previous works, a fiber has failure rate following a power law in its load level with breakdown exponent rho. Surviving fibers under fixed loads have remaining lifetimes that are independent and exponentially distributed. We develop both new asymptotic theories and new computational algorithms that greatly increase the bundle sizes that can be treated in large replications (e.g., one million fibers in thousands of realizations). In particular we develop an algorithm that adapts several concepts and methods that are well-known among computer scientists, but relatively unknown among physicists, to dramatically increase the computational speed with no attendant loss of accuracy. We consider various regimes of rho that yield drastically different behavior as N increases. For 1/2< or =rho< or =1, ELS and LLS have remarkably similar behavior (they have identical lifetime distributions at rho=1) with approximate Gaussian bundle lifetime statistics and a finite limiting mean. For rho>1 this Gaussian behavior also applies to ELS, whereas LLS behavior diverges sharply showing brittle, weakest volume behavior in terms of characteristic elements derived from critical cluster formation. For 0<rho<1/2, ELS and LLS again behave similarly, but the bundle lifetimes are dominated by a few long-lived fibers, and show characteristics of strongest link, extreme value distributions, which apply exactly to rho=0.Physical Review E 02/2001; 63(2 Pt 1):021507. · 2.31 Impact Factor

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