  We examine the equilibrium and stability of an elastocapillary system to
model drying-induced structural failures. The model comprises a circular
elastic membrane with a hole at the center that is deformed by the capillary
pressure of simply connected and doubly connected menisci. Using variational
and spectral methods, stability is related to the slope of equilibrium branches
in the liquid content versus pressure diagram for the constrained and
unconstrained problems. The second-variation spectra are separately determined
for the membrane and meniscus, showing that the membrane out-of-plane spectrum
and the in-plane spectrum at large elatocapillary numbers are both positive, so
that only meniscus perturbations can cause instability. At small
elastocapillary numbers, the in-plane spectrum has a negative eigenvalue,
inducing wrinkling instabilities in thin membranes. In contrast, the smallest
eigenvalue of the meniscus spectrum always changes sign at a pressure turning
point where stability exchange occurs in the unconstrained problem. We also
examine configurations in which the meniscus and membrane are individually
stable, while the elastocapillary system as a whole is not; this emphasizes the
connection between stability and the coupling of elastic and capillary forces.
