Damage cascade in a softening interface

A model describing the damage at an interface which is coupled to an elastic homogeneous block is introduced[ Resorting to a real!space renormalization analysis\ we show that in the absence of heterogeneity localization proceeds through a cascade of bifurcations which progressively concentrates the damage from the global interface to a narrow region leading to a crack nucleation[ The equivalent homogeneous interface behaviour is obtained through this entire cascade\ allowing for the analysis of size e}ects[ When random heterogeneities are introduced in the interface\ prior to the onset of localization damage proceeds by a sequence of avalanches whose mean size diverges at the _rst bifurcation point of the homogeneous interface[ The large scale features of the bifurcation cascade are preserved\ while the details of the late stage are smeared out by the randomness[