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Register a new userBrittle and Non-Brittle Events in a Continuum-Granular Earthquake Experiment
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We report moment distribution results from a laboratory earthquake fault experiment consisting of sheared elastic plates separated by a narrow gap filled with a two dimensional granular medium. Local measurement of strain displacements of the plates at over 800 spatial points located adjacent to the gap allows direct determination of the moments and their spatial and temporal distributions. We show that events consist of localized, larger brittle motions and spatially-extended, smaller non-brittle events. The non-brittle events have a probability distribution of event moment consistent with an $M^{-3/2}$ power law scaling. Brittle events have a broad, peaked moment distribution and a mean repetition time. As the applied normal force increases, there are more brittle events, and the brittle moment distribution broadens. Our results are consistent with mean field descriptions of statistical models of earthquakes and avalanches.
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Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.
Linear fracture mechanics (or at least the initiation part of that theory) can be framed in a variational context as a minimization problem over a SBD type space. The corresponding functional can in turn be approximated in the sense of $Gamma$-convergence by a sequence of functionals involving a phase field as well as the displacement field. We show that a similar approximation persists if additionally imposing a non-interpenetration constraint in the minimization, namely that only nonnegative normal jumps should be permissible. 2010 Mathematics subject classification: 26A45
We analyze large sets of energy-release data created by stress-induced brittle fracture in a pure sapphire crystal at close to zero temperature where stochastic fluctuations are minimal. The waiting-time distribution follows that observed for fracture in rock and for earthquakes. Despite strong time correlations of the events and the presence of large-event precursors, simple prediction algorithms only succeed in a very weak probabilistic sense. We also discuss prospects for further cryogenic experiments reaching close to single-bond sensitivity and able to investigate the existence of a transition-stress regime.
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