Wrinkling of a bilayer membrane

TL;DR

This paper investigates the wrinkling patterns in a bilayer membrane composed of a flexible spherical shell and a stiff strip, combining theory, experiments, and simulations to understand the formation and evolution of wrinkles under tension changes.

Contribution

It provides a comprehensive analysis of wrinkling in bilayer membranes, deriving the wavelength formula and exploring defect formation and secondary wrinkles through combined methods.

Findings

Wavelength of wrinkles is rac{2\u03c0}(B/\sigma)^{1/3}

Defects occur with rapid tension changes

Secondary wrinkles appear at larger tension reductions when B is small

Abstract

The buckling of elastic bodies is a common phenomenon in the mechanics of solids. Wrinkling of membranes can often be interpreted as buckling under constraints that prohibit large amplitude deformation. We present a combination of analytic calculations, experiments, and simulations to understand wrinkling patterns generated in a bilayer membrane. The model membrane is composed of a flexible spherical shell that is under tension and that is circumscribed by a stiff, essentially incompressible strip with bending modulus B. When the tension is reduced sufficiently to a value \sigma, the strip forms wrinkles with a uniform wavelength found theoretically and experimentally to be \lambda = 2\pi(B/\sigma)^{1/3}. Defects in this pattern appear for rapid changes in tension. Comparison between experiment and simulation further shows that, with larger reduction of tension, a second generation of wrinkles with longer wavelength appears only when B is sufficiently small.