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.