Tensile instability of initially spherical balloons

Abstract Using a new elastic constitutive relation for rubber-like materials previously proposed by the author, a large deformation analysis of the inflation of rotationally symmetric balloons is developed and specialized to the inflation of an initially spherical balloon. An investigation of the pressure versus radius characteristic reveals the existence of a local maximum indicating the occurrence of a tensile instability. Observing the form of the total potential energy function at various equilibrium positions yields much insight into the tensile instability phenomenon. An analogy to snap-through buckling is recognized and discussed in detail. Inflation experiments performed with neoprene balloons are found to verify the analytically obtained results. Bifurcations to non-spherical modes in the unstable region, previously investigated by V. I. Feodos'ev by performing a perturbution on the homogeneously deformed non-linear state, are experimentally observed and verified.