The dynamics of cracks in torn thin sheets

TL;DR

This paper investigates how cracks propagate in torn thin sheets by combining elasticity theory with a generalized principle of local symmetry, aligning theoretical predictions with experimental observations.

Contribution

It introduces a generalized criterion for crack path selection in thin sheets, extending existing elasticity models to better match experimental results.

Findings

Qualitative agreement between theory and experiments

Generalized local symmetry criterion for crack paths

Analysis of crack tip singularity with nonlinear effects

Abstract

Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke a generalization of the principle of local symmetry to provide a criterion for path selection and demonstrate qualitative agreement with the experimental findings. The nature of the singularity at the crack tip is studied with and without the interference of nonlinear terms.