Crack propagation in a dynamic fuse model of electromigration

Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes, and human birth

We propose that catastrophic events are "outliers" with statistically different properties than the rest of the population and result from mechanisms involving amplifying critical cascades. We describe a unifying approach for modeling and predicting these catastrophic events or "ruptures," that is, sudden transitions from a quiescent state to a crisis. Such ruptures involve interactions between structures at many different scales. Applications and the potential for prediction are discussed in relation to the rupture of composite materials, great earthquakes, turbulence, and abrupt changes of weather regimes, financial crashes, and human parturition (birth). Future improvements will involve combining ideas and tools from statistical physics and artificial/computational intelligence, to identify and classify possible universal structures that occur at different scales, and to develop application-specific methodologies to use these structures for prediction of the "crises" known to arise in each application of interest. We live on a planet and in a society with intermittent dynamics rather than a state of equilibrium, and so there is a growing and urgent need to sensitize students and citizens to the importance and impacts of ruptures in their multiple forms.

Self-consistent theory of rupture by progressive diffuse damage

We analyze a self-consistent theory of crack growth controlled by a cumulative damage variable d(t) dependent on stress history, in the quasistatic regime where the sound wave velocity is taken as infinite. Depending upon the damage exponent m, which controls the rate of damage dd/dt~sigma(m) as a function of local stress sigma, we find two regimes. For 0<m<2, the model predicts a finite-time singularity. This retrieves previous results by Zobnin for m=1 and by Bradley and Wu for 0<m<2. To improve on this self-consistent theory which neglects the dependence of stress on damage, we apply the functional renormalization method of Yukalov and Gluzman and find that divergences are replaced by singularities with exponents in agreement with those found in acoustic emission experiments. For m>/=2, the rupture dynamics is not defined without the introduction of a regularizing scheme. We investigate three regularization schemes involving, respectively, a saturation of damage, a minimum distance of approach to the crack tip, and a fixed stress maximum. In the first and third schemes, the finite-time singularity is replaced by a crack dynamics defined for all times but which is controlled by either the existence of a microscopic scale at which the stress is regularized or by the maximum sustainable stress. In the second scheme, a finite-time singularity is again found. In the first two schemes within this regime m>/=2, the theory has no continuous limit.