Curved crack paths are predicted by elastic-charges

Abstract: Predicting crack trajectories in brittle solids remains an open challenge in fracture mechanics due to the non-local nature of crack propagation and the way cracks modify their surrounding medium. Here, we develop a framework for analytically predicting crack trajectories, similar to predicting the motion of charged particles in external fields within Newtonian mechanics. We demonstrate that a crack can be described as a distribution of elastic charges, and within the framework of Linear Elastic Fracture Mechanics (LEFM), its interaction with the background stress can be approximated by a singular geometric charge at the crack tip. The cracks motion is then predicted as the propagation of this singular charge within the unperturbed stress field. We apply our approach to study crack trajectories near defects and validate it through experiments on flat elastomer sheets containing an edge dislocation. The experimental results show excellent agreement with theoretical predictions, including the convergence of curved crack trajectories toward a single focal point. We discuss future extension of our theory to the motion of multiple interacting cracks. Our findings highlight the potential of the elastic-charges approach to significantly advance classical fracture mechanics by enabling analytical solutions to problems traditionally requiring numerical methods.