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We propose a novel approach inspired from non-local damage continuum mechanics to describe damage evolution in disordered quasi-brittle solids. Material heterogeneities are introduced at a mesoscopic continuous scale through spatial variations of the resistance to damage. The damage field evolution is computed from irreversible thermodynamics principles by assuming that the elastic energy released during loading is dissipated into failure. The onsets of damage localization and catastrophic failure in the material are studied as a function of the strength of the heterogeneities and the interaction function involved in the non-local formulation of the model. The predictions obtained numerically are explained theoretically for weak heterogeneities using a linear stability analysis and confirmed through a complementary approach based on a global energy minimization. Two distinct quasi-brittle failure behaviors are identified: for interaction functions that impose a reloading of the material points after the occurrence of a damage event, the damage grows rather uniformly in the material until catastrophic failure takes place. On the contrary, when damage events trigger reloading, but also a sufficiently strong unloading in some material regions, catastrophic failure is preceded by a stable regime of damage localization characterized by a length scale emerging from the structure of the load redistribution. Our study reveals the cooperative nature of the damage localization process, showing that quasi-brittle failure emerges from the interaction between the elements constituting the material. It also highlights the central role played by the mechanism of load redistribution that is shown to control the failure behavior of quasi-brittle solids. [ABSTRACT FROM AUTHOR]

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) that accounts for both microstructural disorder and non-local interactions. Its numerical implementation permits performing a complete scaling description of the failure precursors. In particular, we show that their size, duration and spatial extent are related to each other by robust scaling laws and that these three quantities diverge close to failure. 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 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 precursors 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. [ABSTRACT FROM AUTHOR]