Search

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

The failure of brittle solids involves, before macroscopic rupture, power-law distributed avalanches of local rupture events whereby microcracks nucleate and grow, which are also observed in for an elastic interface evolving in a non-homogeneous medium. For this reason, it is tempting to relate failure to the depinning of an elastic interface. Here we compute the elastic kernel of the interface representing the damage field of a brittle solid. In the case of a damage model of rupture under compression, which implements the Mohr-Coulomb criterion at the local scale, we show that the elastic kernel is unstable, and hence is very different from the kernels of usual interfaces. We show that the unstable modes are responsible for the localization of damage along a macroscopic fault observed in numerical simulations. At low disorder, the most unstable mode gives the orientation of the macroscopic fault that we measure in numerical simulations. The orientation of the fault changes when the level of disorder is increased, suggesting a complex interplay of the unstable modes and the disorder.

The Mohr-Coulomb criterion is widely used in geosciences to relate the state of stress at failure to the observed orientation of the resulting faults. This relation is based on the assumption that the fault occurs along a plane that maximizes the Coulomb stress. Here, we test this hypothesis using an elastic, progressive damage model that implements the Mohr-Coulomb criterion at the local scale. We find that the orientation of the fault is not given by the Mohr-Coulomb criterion. Instead, for minimal disorder, it corresponds to the most unstable mode of damage in the model, which we determine through a linear stability analysis of the homogeneously damaged state. Our simulations show that microstructural disorder significantly affects the orientation of the fault, which, however, remains always far from the Mohr-Coulomb prediction.