Axisymmetric elastic membranes subjected to fluid loading

Abstract

We consider axisymmetric isotropic elastic membranes that are loaded by an incompressible liquid. The resulting deformation which contains the liquid is assumed to be axisymmetric. We consider undeformed plane disks of varying thickness and also hemispherical cups. We show how the resulting deformation can be controlled by the initial thickness variation of the disk. In all cases there is a critical loading where the membrane undergoes a very rapid change of shape, from being almost concave to having an hourglass shape. For a hemispherical cup, the deformation produces a wrinkled region which diminishes with increased loading but briefly reappears as the membrane traverses the unstable region. The onset of instability appears to be governed by the equibiaxial deformation at the apex of the deformed container. Instability is initiated when the deformation reaches the corresponding value of the first bifurcation point for a spherical membrane.