"Corner singularities and shape of stretched elastic sheets" by Julien Chopin, Andreea Panaitescu et al.
 

Physics

Corner singularities and shape of stretched elastic sheets

Document Type

Article

Abstract

We investigate the deformation of a longitudinally stretched rectangular sheet which is clamped at two opposite boundaries and free otherwise with experiments, numerical analysis, and asymptotic analysis of the biharmonic elastic equation governing their planar equilibrium configurations. The displacement field of the sheet is measured by tracking embedded fluorescent tracers with a digital image correlation technique. The experiments and numerical finite-element analysis are found to be in overall good agreement except at the very corners where large deformations occur. We find that the deformed sheet can be broadly divided into a uniaxially stretched central region and two clamp-dominated side regions. A subregion characterized by a diverging stress can be identified at each of the four clamped-free corners within the clamp-dominated region. We postulate that the divergence at the corners is regularized by nonlinear elastic deformations occurring in this subregion at the very corners and provide a nontrivial scaling for its size. Within the intermediate corner-dominated subregion, measured displacements grow with distance r from the corners as rα, with power αedges.

Publication Title

Physical Review E

Publication Date

10-17-2018

Volume

98

Issue

4

ISSN

2470-0045

DOI

10.1103/PhysRevE.98.043003

Keywords

elastic deformation, pattern formation, thin films

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