An alternative form of energy density demonstrating the severe strain-stiffening in thin spherical and cylindrical shells

Abstract

The present article investigates an elastic instability phenomenon for internally pressurized spherical thin balloons and thin cylindrical tubes composed of incompressible hyperelastic material. A mathematical model is formulated by proposing a new strain energy density function. In the family of limited elastic materials, many material models exhibit strain-stiffening. However, they fail to predict severe strain-stiffening in a moderate range of deformations in the stress-strain relations. The proposed energy function contains three material parameters and shows substantially improved stain stiffening properties than the limited elastic material models. The model is further applied to explore the elastic instability phenomenon in spherical and cylindrical shells. The findings are compared with other existing models and validated with experimental results. The model shows better agreement with experimental results and exhibits a substantial strain-stiffening effect than the current models.