Title: Shortest paths govern fracture nucleation in thermoset networks

Abstract: In this work, we introduce a predictive approach for determining fracture nucleation in thermosets based on shortest paths (SPs) of the network topology. This method enumerates SP sets in networks with periodic boundary conditions, with applications to both all-atom and coarse-grained simulations. We find that network fracture is most likely to nucleate on the first (shortest) SP and the strain at nucleation is linearly correlated with the topological path length. Subsequent fracture events are dictated by the instantaneous SP of partially broken networks. We further quantify the length scale dependence of SP distributions, introducing a means of bridging simulated and experimental fracture profiles.