Predicting Crack Trajectory Using "Elastic Charges"

Predicting the trajectory of a crack in residually stressed solids is a formidable challenge in the field of solid mechanics. A central difficulty arises from the dynamic nature of the boundary conditions due to crack evolution. Here we introduce a method that avoids this difficulty by describing cracks as distributed induced "elastic charges." We show that quasi-static crack evolution is equivalent to a propagating non-topological dislocation. We implement our method to predict the trajectory of a crack in the vicinity of a topological defect that acts as an internal source of stress. Our theory is supported by a good agreement between the predicted trajectories and the experimental measurements of cracks moving in dislocated elastic media.