Swelling and inflation of a toroidal gel balloon

Abstract

This work mainly focuses on the free swelling and inflation mechanics of a hyperelastic homogeneous and isotropic gas-filled toroidal gel balloon of an initially circular cross-section. Two compressible hyperelastic material models, namely neo-Hookean and Gent, are considered with Flory–Huggins mixing energy. Mechanics of free swelling configurations are studied using equilibrium equations obtained for incompressible and compressible axisymmetric inflation. The two-point boundary value problem of the balloon was solved using the Nelder–Meads search technique by constructing an optimization problem. Non-uniform solvent concentration is resulted in the meridional direction for the equilibrium swelling and inflation. For the neo-Hookean material, the instant/delayed burst phenomenon is concluded for almost all the geometric and material parametric ranges due to the softening type nonlinearity. On the other hand, for the Gent material model, instant/delayed short burst phenomenon is found for a specific range of dimensionless material constants. The inflation pressure range for the burst phenomenon and equilibrium swelling is identified for particular material parametric ranges. The critical pressure for the delayed short burst is roughly estimated and found to be highly dependent on the nonlinear nature of the swollen toroidal gel balloon inflation pressure-stretch curve. Also, deswelling is observed at the larger inflation stretch values of the gel.