Inflation and Bifurcation of Thick-Walled Compressible Elastic Spherical Shells

Abstract

The problem of inflation for a thick-walled compressible, isotropic, hyperelastic, spherical shell is considered. First we give a new class of strain–energy functions for which analytic solutions to the spherically symmetric problem can be obtained. These solutions are compared with the existing solutions for harmonic materials. Secondly we obtain numerical results for the aspherical bifurcation problem. A number of different strain–energy functions are considered and all show the same qualitative features as those demonstrated by incompressible materials. We show that a decrease in the bulk modulus of the material has a stabilizing effect, in that critical values of the deformation are increased.