Spatially Weighted Betweenness Centrality for Predicting Fracture in End-Linked Polymer Networks

The macroscopic mechanical properties of polymer networks are closely linked to their microscopic topological structures. Although traditional geodesic edge betweenness centrality (GEBC) can effectively predict damage sites in disordered solids, its predictive accuracy is limited because it is based solely on topological connectivity. In this study, by introducing the spatial orientation and geometric scale of microscopic segments, we propose orientation-weighted betweenness centrality (OBC) and distance-weighted betweenness centrality (DBC). Molecular dynamics (MD) simulations demonstrated that the initial-state OBC offers superior predictive power for final fracture locations, whereas the DBC correlates more strongly with fractures during the later stages of stretching, revealing the evolution of fracture modes from local damage to long-range cooperative failure. Further analysis using the topological pair-correlation function (TPCF) revealed that a local fracture pattern of “nearest-neighbor repulsion and next-nearest-neighbor attraction” emerged before yielding, which gradually transformed into a long-range, positively correlated cooperative failure. This study not only validates the superiority of composite metrics integrating topological and geometric information in predicting polymer failure but also clarifies the cross-scale mechanism by which microscopic damage evolves into macroscopic cracks via network reorganization. These findings provide a new theoretical foundation and a characterization tool for designing high-performance, high-toughness polymer networks.