Axisymmetric instability of soft elastic tubes under axial load and surface tension

Abstract Elastic tubes can experience surface instabilities when compressed beyond a critical strain, referred to as Wilkes instability herein. Soft materials may undergo the Rayleigh–plateau instability which is driven by surface tension. However, the surface instability of soft elastic tubes can be impeded by the coexistence of axial compression and surface tension. In this paper, we adopted an analytical framework for predicting the surface instability of an incompressible tube accounting for both axial loading and surface tension. A general solution in a mixed cylindrical coordinate is derived for determining isochoric transformations based on energy variational method. A linear perturbation analysis was performed to find out the critical elasto-capillary number and axial stretch for the onset of the instability. Cylindrical tubes with different thickness, i.e., the ratio of outer to inner radii, are investigated. We find that thinner tubes are more likely to experience surface instability than thicker ones, as validated by finite element simulations. We conclude that a compressive strain could prevent the Rayleigh–plateau instability induced by surface tension, while stretching will favor it. Similarly, the surface tension behaves as a barrier to the formation of compression-induced Wilkes instability.