Critical Sensitivity and Trans-Scale Fluctuations in Catastrophic Rupture

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)

Multiscale Coupling: Challenges and Opportunities

Multiscale coupling is ubiquitous in nature and attracts broad interests of scientists from mathematicians, physicists, machinists, chemists to biologists. However, much less attention has been paid to its intrinsic implication. In this paper, multiscale coupling is introduced by studying two typical examples in classic mechanics: fluid turbulence and solid failure. The nature of multiscale coupling in the two examples lies in their physical diversities and strong coupling over wide-range scales. The theories of dynamical system and statistical mechanics provide fundamental methods for the multiscale coupling problems. The diverse multiscale couplings call for unified approaches and might expedite new concepts, theories and disciplines

Experimental Evidence of Critical Sensitivity in Catastrophe

The paper presents an experimental study on critical sensitivity in rocks. Critical sensitivity means that the response of a system to external controlling variable may become significantly sensitive as the system approaches its catastrophic rupture point. It is found that the sensitivities measured by responses on three scales (sample scale, locally macroscopic scales and mesoscopic scale) display increase prior to catastrophic transition point. These experimental results do support the concept that critical sensitivity might be a common precursory feature of catastrophe. Furthermore, our previous theoretical model is extended to explore the fluctuations in critical sensitivity in the rock tests

Cluster statistical thermodynamics (CST) - To efficiently calculate quasi-static deformation at finite temperature based on molecular potential

For quasi-static deformations in engineering practice, molecular dynamics (MD) simulation requires computation resources that are not affordable even with ever-increasing computing power. In order to overcome this weakness, we developed a new method called cluster statistical thermodynamics (CST). By taking the advantage of statistical thermodynamics and adopting finite-element interpolation, the new approach can not only simulate quasi-static deformation but have very high computing efficiency. The new method is based on molecular potentials as MD does, but statistical thermodynamics help us greatly reduce the tedious calculation of thermal fluctuations of molecules. Therefore, the new method appears to be superior to MD in the simulations of quasi-static deformation. Especially CST works much more efficiently than MD with much less storage space and CPU time. In this paper, we illustrate the new methodology by means of some examples of two-dimensional quasi-static tensile process at 300 K. It is found that the results obtained with CST are in good agreement with those obtained by fully atomistic simulations and CST is 600 times faster than MD. Hence, the new method seems to be a very efficient and promising approach to numerical simulations of solid deformations under quasi-static loadings and at finite temperatures, based on molecular potentials