Coming up next
2026-06-10 - 11:00 @ BM.2.27
SLAM: talk by Oran Szachter (Luca's guest)
A Geometric Approach to Fracture Mechanics
Fracture occurs across a vast range of systems, from brittle solids to soft and complex materials. The classical framework, Linear Elastic Fracture Mechanics (LEFM), assumes purely elastic, linearly strained media, assumptions that break down in materials with internal structure. Even within its domain of validity, analytical predictions of crack trajectories remain an open challenge.
In this talk, I present two works that extend fracture mechanics using the language of elastic charges. First, by describing a crack as a distribution of elastic charges, we predict crack trajectories in residually stressed media. We then extend the J-integral, a classical measure of toughness, to materials with internal degrees of freedom such as granular packings, knitted fabrics, and biological tissues. By modeling plastic rearrangements as induced elastic charges, we predict whether they toughen or weaken the materials. Together, these approaches offer a unified geometric description of fracture.