Failure as a critical phenomenon in a progressive damage model
Résumé
The critical point hypothesis for fracture is tested using a progressive damage model. The advantage of the present model, based on continuum mechanics, is the possibility of tracking the approach to final failure in terms either of discrete events (the avalanches) or of the resulting continuous strain field. Different but actually closely linked phenomena are reported. In terms of damage avalanches, power law distributions of avalanche sizes and energies are observed associated with a finite size scaling. The finite size scaling is also observed for the spatial correlations of damage events. A divergence of the correlation length is reported in the vicinity of final failure, from a correlation analysis of discrete events and from a scaling analysis of the continuous strain rate field. We also show that multifractal properties of the deformation emerge from the long-range elastic interactions that occur near final failure. All of these results argue for a critical point interpretation of failure. Finally, we discuss the implications of our results for the criticality of fracture and deformation of geophysical objects, and for associated precursory phenomena.