Energetic developments in fracture

Marder, Michael

doi:10.1038/381275a0

Cited by 9 publications

(5 citation statements)

References 7 publications

(5 reference statements)

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“…For the external force on upper and lower boundaries, from a systematic study on a triangular lattice, it has been discovered that the crack tip moves only when the external driving force is strong enough, for C > 1 [17]. For the square lattice, we observe a similar phenomenon.…”

Section: A Slepyan Model For Fracture In Two Space Dimensionssupporting

confidence: 54%

A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations

Tang

Hou

Liu

2006

Journal of Computational Physics

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In this paper, we propose a pseudo-spectral multiscale method for simulating complex systems with more than one spatial scale. Using a spectral decomposition, we split the displacement into its mean and fluctuation parts. Under the assumption of localized nonlinear fluctuations, we separate the domain into an MD (Molecular Dynamics) subdomain and an MC (MacrosCopic) subdomain. An interfacial condition is proposed across the two scales, in terms of a time history treatment. In the special case of a linear system, this is the first exact interfacial condition for multiscale computations. Meanwhile, we design coarse grid equations using a matching differential operator approach. The coarse grid discretization is of spectral accuracy. We do not use a handshaking region in this method. Instead, we define a coarse grid over the whole domain and reassign the coarse grid displacement in the MD subdomain with an average of the MD solution. To reduce the computational cost, we compute the dynamics of the coarse grid displacement and relate it to the mean displacement. Our method is therefore called a pseudo-spectral multiscale method. It allows one to reach high resolution by balancing the accuracy at the coarse grid with that at the interface. Numerical experiments in one-and two-space dimensions are presented to demonstrate the accuracy and the robustness of the method.

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Section: A Slepyan Model For Fracture In Two Space Dimensionssupporting

confidence: 54%

A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations

Tang

Hou

Liu

2006

Journal of Computational Physics

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“…However, is it possible to predict a specific earthquake in a laboratory or in computer simulations? In a laboratory and simulations, a crack develops instabilities which make its propagation highly chaotic and unpredictable (Abraham 1996;Marder 1996;Marder & Fineberg 1996;Abraham et ul. 1997).…”

Section: Specific-earthquake Predictionmentioning

confidence: 99%

Are earthquakes predictable?

Kagan

1997

Geophysical Journal International

155

109

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S U M M A R YThe answer to the above question depends on the definition of earthquake prediction. We discuss several definitions and possible classifications of earthquake prediction methods. We also consider various measures of prediction efficiency, review several recent examples of earthquake prediction, and describe the methods that can be used to verify prediction schemes. We conclude that an empirical search for earthquake precursors that forecast the size of an impending earthquake has been fruitless. Despite considerable effort in several countries, no statistically rigorous validation of proposed precursory phenomena is available; therefore, reported cases of precursors can be explained by random noise or by chance coincidence. We present evidence that earthquakes are non-linear, chaotic, scale-invariant phenomena. The most probable consequence of earthquake self-similarity is a lack of earthquake predictability as popularly defined, that is a forecast of a specific individual earthquake. Many small earthquakes occur throughout any seismic zone, demonstrating that the critical conditions for earthquake nucleation are satisfied almost everywhere. Apparently, any small shock can grow into a large event. Thus, it is likely that an earthquake has no preparatory stage. This sceptical view of current earthquake prediction efforts should not be interpreted as a statement that any further attempts to mitigate the destructive effects of earthquakes are futile. The seismic-moment conservation principle, when combined with geodetic deformation data, offers a new way to evaluate the seismic hazard, not only for tectonic plate boundaries, but also for areas of low seismicity, that is the interiors of continents. Earthquake clustering with a power-law temporal decay (Omori's law) can be used to estimate the rate of future earthquake ocurrence. Realtime seismology can facilitate relief efforts after large earthquakes and eventually provide an immediate warning of severe shaking a few seconds or tens of seconds before the shaking starts.

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“…The propagation of cracks in such media has been investigated recently using developments in nonlinear physics [19][20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Fracture patterns induced by desiccation in a thin layer

Kitsunezaki

1999

Phys. Rev. E

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We study a theoretical model of mud cracks, that is, the fracture patterns resulting from the contraction with drying in a thin layer of a mixture of granules and water. In this model, we consider the slip on the bottom of this layer and the relaxation of the elastic field that represents deformation of the layer. Analysis of the one-dimensional model gives results for the crack size that are consistent with experiments. We propose an analytical method of estimation for the growth velocity of a simple straight crack to explain the very slow propagation observed in actual experiments. Numerical simulations reveal the dependence of qualitative nature of the formation of crack patterns on material properties.

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Energetic developments in fracture

Cited by 9 publications

References 7 publications

A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations

A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations

Are earthquakes predictable?

Fracture patterns induced by desiccation in a thin layer

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