We consider the eversion problem for highly compressible hyperelastic
thick-walled cylinders. We focus attention on two features of such pro
blems that are not adequately described by standard analysis. We inves
tigate, first, closure of the cavity for sufficiently thick tubes and,
second, the instability of relatively thin tubes. We find that the cl
osure of the cavity can be ascribed to the fact that actual foam cylin
ders behave differently in tension and compression. However, the insta
bility of thinner cylinders seems to be governed by some other mechani
sm. In the course of the analysis, we show how exact solutions to the
equilibrium equation for the eversion problem can be generated. Unfort
unately such solutions are not compatible with the boundary conditions
.