From Fracture Mechanics to Electrostatics And Back Again

Cracks are nature’s master sculptors, carving intricate patterns as materials break. Yet predicting the path a crack will take, especially along curved trajectories, remains a central challenge in fracture mechanics. Traditional approaches rely on heavy numerical simulations, due to the iterative nature of cracks as they modify the medium in which they move, thus struggling to capture the elegant simplicity we often find in the motion of particles under Newton’s laws.

In this talk, I will show how a geometric perspective leads to a surprising and powerful analogy: cracks behave like moving point charges in an elastic field. This connection breathes new life into the problem, linking it to a historical anecdote about conducting needles, and opening new doors to the physics of mechanical screening. I will briefly explore how this viewpoint sheds light on the anomalous behavior of disordered solids, and the nonlinear responses of mechanical metamaterials.
Returning full circle, I will present a new theoretical framework for predicting curved crack paths, not through iteration or simulation but through direct analytical insight, and share experiments that strikingly confirm these predictions.
Together, these ideas reveal a hidden unity between fracture, geometry, and field theory, offering a new way to understand how materials break, deform, and transform.