Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

Xia, Mingji; Fang, Ke; Jie, Bai; Bai, Yilong

doi:10.1016/s0375-9601(97)00719-6

Cited by 21 publications

(19 citation statements)

References 3 publications

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“…For instance, some precursors approaching critical failure were found from an analysis of acoustic emission signals [8,10]. Also discovered were several general features that might be significantly enhanced near catastrophic failure [29,30]. Furthermore, the scaling behaviours, as discussed above, highlight the possibility that the material property at the macroscopic scale could be insensitive to details on the microscale.…”

Section: Discussionmentioning

confidence: 94%

“…Or conversely, we ask to what extent the predictability of a final catastrophic failure is dependent on the sensitivity of the microcrack system to disorder or stochastic fluctuation [29,30]. For this purpose, we just randomly change the spatial position of the nucleated microcrack that induces the avalanche (catastrophic failure), and observe the spatiotemporal distribution.…”

Section: Resultsmentioning

confidence: 99%

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Fractals and scaling in fracture induced by microcrack coalescence

Mai

Bai

2005

Philosophical Magazine Letters

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A numerical model is proposed to simulate fracture induced by the coalescence of numerous microcracks, in which the condition for coalescence between two randomly nucleated microcracks is determined in terms of a load-sharing principle. The results of the simulation show that, as the number density of nucleated microcracks increases, stochastic coalescence first occurs followed by a small fluctuation, and finally a newly nucleated microcrack triggers a cascade coalescence of microcracks resulting in catastrophic failure. The fracture profiles exhibit self-affine fractal characteristics with a universal roughness exponent, but the critical damage threshold is sensitive to details of the model. The spatiotemporal distribution of nucleated microcracks in the vicinity of critical failure follows a power-law behaviour, which implies that the microcrack system may evolve to a critical state.

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Section: Discussionmentioning

confidence: 94%

Section: Resultsmentioning

confidence: 99%

Fractals and scaling in fracture induced by microcrack coalescence

Mai

Bai

2005

Philosophical Magazine Letters

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“…For multiscale problems in far from equilibrium cases the physical mechanisms or the dynamics may differ on different scales [5], and the interaction between different scales is usually strong and/or sensitive [6]. As a result, the similar solutions in mechanics, which root in identical physics at various scales, are questionable in these problems.…”

Section: Introductionmentioning

confidence: 99%

Trans-scale Coupling in Multiscale Simulations

Feng

Wang

Xia

et al. 2006

Int J Mult Comp Eng

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“…This is quite similar to rupture in heterogeneous brittle media. Rupture appears to be a catastrophe transition (BAI et al, 1994;WEI et al, 2000) and the threshold of catastrophe shows uncertainty (XIA et al, 1997;XIA et al, 2000). It is insufficient to represent the rupture of disordered heterogeneous media by only macroscopically averaged properties (SAHIMI et al, 1993;MEAKIN, 1991;IBNABDELJALIL et al, 1997;CURTIN, 1997).…”

Section: Introductionmentioning

confidence: 99%

Critical Sensitivity and Trans-scale Fluctuations in Catastrophic Rupture

Xia

Wei

et al. 2002

Earthquake Processes: Physical Modelling, Numerical Simulation and Data Analysis Part II

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-Rupture in the heterogeneous crust appears to be a catastrophe transition. Catastrophic rupture sensitively depends on the details of heterogeneity and stress transfer on multiple scales. These are difficult to identify and deal with. As a result, the threshold of earthquake-like rupture presents uncertainty. This may be the root of the difficulty of earthquake prediction. Based on a coupled pattern mapping model, we represent critical sensitivity and trans-scale fluctuations associated with catastrophic rupture. Critical sensitivity means that a system may become significantly sensitive near catastrophe transition. Trans-scale fluctuations mean that the level of stress fluctuations increases strongly and the spatial scale of stress and damage fluctuations evolves from the mesoscopic heterogeneity scale to the macroscopic scale as the catastrophe regime is approached. The underlying mechanism behind critical sensitivity and trans-scale fluctuations is the coupling effect between heterogeneity and dynamical nonlinearity. Such features may provide clues for prediction of catastrophic rupture, like material failure and great earthquakes. Critical sensitivity may be the physical mechanism underlying a promising earthquake forecasting method, the load-unload response ratio (LURR).

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Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

Cited by 21 publications

References 3 publications

Fractals and scaling in fracture induced by microcrack coalescence

Fractals and scaling in fracture induced by microcrack coalescence

Trans-scale Coupling in Multiscale Simulations

Critical Sensitivity and Trans-scale Fluctuations in Catastrophic Rupture

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