Finite-distance singularities in the tearing of thin sheets

TL;DR

This paper studies how two cracks in a thin sheet interact and converge, revealing geometry-dependent singularities that depend on the balance of stretching and bending near crack tips.

Contribution

It introduces experimental geometries to observe finite-distance singularities in crack interactions and derives scaling laws based on sheet mechanics.

Findings

Cracks converge along self-similar paths and annihilate.

Singularity exponents depend on geometry.

Scaling arguments match experimental observations.

Abstract

We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.