Forecasting failure locations in 2-dimensional disordered lattices

Abstract

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. arXiv:1812.08025v3 [cond-mat.soft]

Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks

“…Interestingly, link-based centrality measures have received very little attention instead. A notable exception is the definition of edge betweenness (38) and its recent application to failure prediction in network models of materials and structures under mechanical load (39,40). Basic phenomena such as wave propagation, simple in Euclidean geometries, may need even more complex tools: The systematic advancement of a wave front implies the systematic usage of certain links, and systematically in one direction.…”

Network analysis predicts failure of materials and structures

“…Despite their general and abstract nature, network analytic concepts are often useful tools to analyze physical processes on networks, which may strongly depend on structural properties of the network and their evolution. Berthier et al (1) demonstrate this by forecasting failure locations in loadcarrying lattice structures based on so-called geodesic edge betweenness centrality (GEBC).…”

“…Edge betweenness centrality ranks the importance of edges based on the fraction of shortest paths between any 2 points on a network that traverse a given edge (2), and Berthier et al (1) demonstrate that a large GEBC value serves as a good predictor for failure locations in disordered beam networks subjected to tensile or compressive loading: They performed an experiment where they successively loaded a network and recorded the sequence of beam failures, while analyzing the concomitant evolution of the centrality pattern. They show that high GEBC correlates strongly with beam failure and achieves prediction scores that are comparable to those obtained from a simple physical model of load redistribution.…”

“…1). Such networks need not, of necessity, consist of networked material beams as present in the structures studied by Berthier et al (1) or, in a more regular version, in the structure of the Eiffel tower ( Fig. 1A) and of many additively manufactured metamaterials (refs.…”

“…Load transfer in granular assemblies is controlled by force chain networks (Fig. 1C), which served as templates for the beam networks studied by Berthier et al (1). Porous structures under load develop, in the approach to failure, stress transfer chains that can be analyzed along very similar lines (8).…”