Axial and circumferential buckling of a hyperelastic tube under restricted compression

Axial compression of a rubber tube where the movement of the outer surface is restricted is an important procedure used to seal a packer. Instabilities may cause the seal to fail. In this paper, we study the bifurcations of a hyperelastic tube under restricted compression and consider both axial and circumferential modes. Bifurcation condition is numerically determined and it is found that the critical stretch is a decreasing function of the ratio of inner and outer radii A∕B. Furthermore, the critical mode number is always finite for both modes. In particular, a transition between axial and circumferential modes occurs when A∕B passes through a critical value of 0.6716. A WKB analysis is carried out to provide an asymptotic expression for the axial stretch λz when the mode number n is large. Finally an application of our results in sealing devices is discussed.