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We investigate numerically and theoretically the precursory intermittent activity characterizing the preliminary phase of damage accumulation prior to failure of quasi-brittle solids. We use a minimal but thermodynamically consistent model of damage growth and localization developed by Berthier et al. (2017). The approach accounts for both microstructural disorder and non-local interactions and permits inferring a complete scaling description of the spatio-temporal structure of failure precursors. By developing a theoretical model of damage growth in disordered elasto-damageable specimen, we demonstrate that these scaling relations emerge from the physics of elastic manifolds driven in disordered media, while the divergence of these quantities close to failure is reminiscent of the loss of stability of the specimen at the localization threshold. Our study sorts out a long-standing debate on the nature of the compressive failure point and the origin of the universal statistics of the precursors preceding it. Our analysis rules out a critical-point scenario in which the divergence of the precursor size close to failure is signature of a second-order phase transition governed by the microstructural disorder. Instead, we show that while the jerky evolution of damage prior to failure results from the presence of material disorder, the latter does not significantly change the nature of the localization process, which is an instability well described by standard bifurcation theory of homogeneous systems. Finally, we harness our detailed understanding of the precursory statistics to design a methodology to estimate the residual lifetime of a structure from the statistical analysis of precursors. This method relevant for structural health monitoring is shown to perform rather accurately on our data., Comment: 26 pages, 7 figures

Forecasting fracture locations in a progressively failing disordered structure is of paramount importance when considering structural materials. We explore this issue for gradual deterioration via beam breakage of two-dimensional disordered lattices, which we represent as networks, for various values of mean degree. We study experimental samples with geometric structures that we construct based on observed contact networks in 2D granular media. We calculate geodesic edge betweenness centrality, which helps quantify which edges are on many shortest paths in a network, to forecast the failure locations. We demonstrate for the tested samples that, for a variety of failure behaviors, failures occur predominantly at locations that have larger geodesic edge betweenness values than the mean one in the structure. Because only a small fraction of edges have values above the mean, this is a relevant diagnostic to assess failure locations. Our results demonstrate that one can consider only specific parts of a system as likely failure locations and that, with reasonable success, one can assess possible failure locations of a structure without needing to study its detailed energetic states., Comment: Extended discussion, added supplementary information

In ordinary solids, material disorder is known to increase the size of the process zone in which stress concentrates at the crack tip, causing a transition from localized to diffuse failure. Here, we report experiments on disordered 2D lattices, derived from frictional particle packings, in which the mean coordination number $\langle z \rangle$ of the underlying network provides a similar control. Our experiments show that tuning the connectivity of the network provides access to a range of behaviors from brittle to ductile failure. We elucidate the cooperative origins of this transition using a frictional pebble game algorithm on the original, intact lattices. We find that the transition corresponds to the isostatic value $\langle z \rangle = 3$ in the large-friction limit, with brittle failure occurring for structures vertically spanned by a rigid cluster, and ductile failure for floppy networks containing nonspanning rigid clusters. Furthermore, we find that individual failure events typically occur within the floppy regions separated by the rigid clusters.