  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.

Soft Condensed Matter