Energy dissipation statistics in the random fuse model

Picallo, Clara B.; López, Juan M.

doi:10.1103/physreve.77.046114

Cited by 8 publications

(14 citation statements)

References 44 publications

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“…Variations in the power-law shape and tail are shown to be related to the presence of an exponential cut-off that depends on the finite size of the model and diverges as the critical point is approached. The finite rate of the loading has also been proposed to induce a cut-off of the power-law distribution for largest size events [39,36]. The evoked mechanism is that the loading rate should be infinitely small, or small enough, for allowing the long range interaction that permits the emergence of avalanches at all scales.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Variability in the power-law distributions of rupture events

Amitrano

2012

Eur. Phys. J. Spec. Top.

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Rupture events, as the propagation of cracks or the sliding along faults, associated with the deformation of brittle materials are observed to obey power-law distributions. This is verified at scales ranging from laboratory samples to the Earth's crust, for various materials and under various loading modes. Besides the claim that this is a universal characteristic of the deformation of heterogeneous media, spatial and temporal variations are observed in the exponent and tail-shape. These have considerable implications for the ability and the reliability of forecasting large events from smaller ones. There is a growing interest in identifying the factors responsible for these variations. In this present work, we first present observations at various scales (laboratory tests, field experiments, landslides, mining induced seismicity, crustal Earthquakes) showing that substantial variations exist in both the slope and the tailshape of the rupture event size distribution. This review allows us to identify potential explanations for these variations (incorrect statistical methods, heterogeneity, stress, brittle/ductile transition, finite size effects, proximity to the failure). A possible link with the critical point theory is also drawn showing that it is able to explain a part of the observed variations considering the distance to the critical point. Using numerical simulations of progressive failure we investigate the role of mechanical properties on the powerlaw distributions. The results of simulations agree with the critical point theory for various macroscopic behaviors ranging from ductility to brittleness providing a unified framework for the understanding of power-law variability observed in rupture phenomena.

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Section: Numerical Simulationsmentioning

confidence: 99%

“…Alternatively, the loading induced by the cutting at the front of the excavation can be considered as fast enough for activating viscous dissipation inducing a cut-off related to finite loading rate [36,39].…”

Section: Finite Size Effectmentioning

confidence: 99%

Variability in the power-law distributions of rupture events

Amitrano

2012

Eur. Phys. J. Spec. Top.

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“…These avalanches often follow a power-law distribution over many decades, signalling the existence of a nonequilibrium critical depinning transition at the onset of motion. Systems showing this scaling behavior include chargedensity waves, fluid interfaces, magnetic domain walls, granular media, foams, crystals, amorphous metals and the earth's crust [1][2][3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…Theoretical studies of avalanches have generally considered lattice-based models with simple site interaction rules [1,5,8,11,13,[15][16][17][18][19][20][21][22][23]. These models are computationally and analytically tractable, but have the limitation that position and stress changes are discrete.…”

Section: Introductionmentioning

confidence: 99%

Effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions

2013

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Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal quasistatic limit. In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop. Scaling exponents are determined using finite-size scaling for systems with 10(3)-10(6) particles. Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two regimes. For each universality class, the exponent describing the avalanche distributions is the same in two and three dimensions. The spatial extent of plastic deformation is proportional to the energy dissipated in an avalanche. Both rise much more rapidly with system size in the underdamped limit where inertia is important. Inertia also lowers the mean energy of configurations sampled by the system and leads to an excess of large events like that seen in earthquake distributions for individual faults. The distribution of stress values during shear narrows to zero with increasing system size and may provide useful information about the size of elemental events in experimental systems. For overdamped and crossover systems the stress variation scales inversely with the square root of the system size. For underdamped systems the variation is determined by the size of the largest events.

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“…A Fourier number of 0.1 was selected for the case where the energy dissipated is maximized. 26,27 The design trade-off is based on the optimization of structure dimensions as a decrease in the fuse cross-sectional area allows for an increase in the heat dissipation at the expense of a higher current density. The optimization, therefore, relies on finding the right fuse dimensions that would provide enough Joule heating to reliably break the silicon nitride membrane.…”

Section: Design Of Drug Delivery Devicementioning

confidence: 99%

Electro-thermally induced structural failure actuator (ETISFA) for implantable controlled drug delivery devices based on Micro-Electro-Mechanical-Systems

et al. 2010

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A new electro-thermally induced structural failure actuator (ETISFA) is introduced as an activation mechanism for on demand controlled drug delivery from a Micro-Electro-Mechanical-System (MEMS). The device architecture is based on a reservoir that is sealed by a silicon nitride membrane. The release mechanism consists of an electrical fuse constructed on the membrane. Activation causes thermal shock of the suspended membrane allowing the drugs inside of the reservoir to diffuse out into the region of interest. The effects of fuse width and thickness were explored by observing the extent to which the membrane was ruptured and the required energy input. Device design and optimization simulations of the opening mechanism are presented, as well as experimental data showing optimal energy consumption per fuse geometry. In vitro release experiments demonstrated repeatable release curves of mannitol-C(14) that precisely follow ideal first order release kinetics. Thermally induced structural failure was demonstrated as a feasible activation mechanism that holds great promise for controlled release in biomedical microdevices.

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Energy dissipation statistics in the random fuse model

Cited by 8 publications

References 44 publications

Variability in the power-law distributions of rupture events

Variability in the power-law distributions of rupture events

Effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions

Electro-thermally induced structural failure actuator (ETISFA) for implantable controlled drug delivery devices based on Micro-Electro-Mechanical-Systems

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