Inflation of spherical rubber balloons

When a spherical rubber balloon of the sort used in meteorological applications is inflated, the onset of aspherical deformation is observed after the pressure maximum has been attained. Upon further inflation the balloon regains its spherical shape. Here, the rubber balloon is idealized as an elastic membrane and inflation is taken to be accomplished by a prescribed increase in enclosed volume. The axisymmetric equilibrium states of slightly imperfect membranes are determined numerically by means of the Ritz-Galerkin method. Several particular material models representative of the behavior of rubberlike solids are employed in order to illustrate a number of feautres associated with the aspherical deformation.