Inflation and deflation of a pseudo-elastic spherical shell

Abstract A constitutive model for finite deformation equibiaxial stretch of an incompressible isotropic pseudo-elastic solid is proposed, and this is used to consider cycles of finite deformation inflation and deflation, of a pseudo-elastic thick-walled spherical shell. The model is based on a non-linear finite deformation elastic stress–stretch relation for loading from the unstressed state and another non-linear stress–stretch relation for unloading which results in a hysteresis effect with no residual deformation at zero stress. Cycles of loading and reloading from partially unloaded states are also incorporated in the model. The method of solution of the thick-walled spherical shell problem uses the stress–stretch relation for equibiaxial tension and can be adapted to use experimentally determined stress–stretch relations. Numerical results are presented for a particular case of the equibiaxial tension model which has a Mooney–Rivlin stress–stretch relation for loading from the unstressed state and modifications of the Mooney–Rivlin relation for unloading or reloading from a partially unloaded state.