Curved crack paths are predicted by elastic-charges

Predicting crack trajectories in brittle solids remains an open challenge due to their non-local nature and the way they modify the surrounding medium. Here, we develop a framework for analytically predicting crack paths, analogous to predicting particle motion in Newtonian mechanics. We show that a crack can be described as a distribution of elastic charges, with its interaction with background stress dominated by a singular geometric charge at the crack tip. The crack’s motion is then governed by the propagation of this singular charge. We apply our analytical 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 focal point. We conclude by discussing the analytical power of our method within Linear Elastic Fracture Mechanics and its extension to multiple interacting cracks.