On the eversion of incompressible elastic spherical shells

We consider the problem of everting spherical shells of incompressible, isotropic hyperelastic material. Firstly, we show that there exists a unique spherically symmetric everted solution for all shell thicknesses provided only that the material satisfies the Baker-Ericksen inequalities. We also give a sufficient condition, satisfied by many materials, which ensures that the shell contains a cavity on eversion. Secondly we look at the bifurcation problem. We find that thicker shells will undergo a bifurcation on eversion and so we would only expect to see spherically symmetric solutions for thinner shells.