Inflation and deflation of a pseudo-elastic spherical shell

A constitutive model for finite deformation equibiaxial stretch of an incom pressible isotropic pseudo-elastic solid is proposed, and this is used to c onsider cycles of finite deformation inflation and deflation, of a pseudo-e lastic thick-walled spherical shell. The model is based on a non-linear fin ite deformation elastic stress-stretch relation for loading from the unstre ssed state and another non-linear stress-stretch relation for unloading whi ch results in a hysteresis effect with no residual deformation at zero stre ss. Cycles of loading and reloading from partially unloaded states are also incorporated in the model. The method of solution of the thick-walled sphe rical shell problem uses the stress-stretch relation for equibiaxial tensio n and can be adapted to use experimentally determined stress-stretch relati ons. Numerical results are presented for a particular case of the equibiaxi al tension model which has a Mooney-Rivlin stress-stretch relation for load ing from the unstressed state and modifications of the Mooney-Rivlin relati on for unloading or reloading from a partially unloaded state. (C) 1999 Els evier Science Ltd. All rights reserved.