Self-organized criticality of deformation and prospects for fracture prediction

The paper considers common nonlinear characteristics of inelastic deformation and fracture of loaded solids and similarity of numerical solutions of a nonlinear system of relevant partial differential equations. The self-similarity of inelastic strain and damage accumulation in the entire hierarchy of scales-from interatomic distances up to tectonic faults of many thousands of kilometers in the Earth crust-ensures qualitative similarity of fracture scenarios whatever the scale of deformation and rheology of a medium. The common properties of deformed systems are spatial localization of inelastic strain and damage accumulation in the entire hierarchy of scales, further temporal strain localization as a superfast autocatalytic blow-up process, slow dynamics (deformation fronts or slow motions), and strain activity migration due to long-range space-time correlations over the entire hierarchy of scales. Thus, fracture evolves as a sequence of catastrophes of increasing scales up to macroscales. It is shown that self-organized criticality of any deformed system does not exclude the possibility to predict the time and the place of a future catastrophic event. Precursors of similar large-scale events can be (i) frozen strain activity in the immediate vicinity of a formed main crack or fault and (ii) generation of trains of deformation fronts (damage fronts) in this region and their flow toward the site of a formed main crack (fault).