Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes

TL;DR

This paper investigates the post-bifurcation behavior of soft cylindrical tubes under surface tension, revealing how localized bulging or necking develops and transitions into a two-phase state through theoretical analysis and FEM simulations.

Contribution

It provides a weakly non-linear analysis of the bifurcation process, identifying conditions for localized instabilities and the emergence of kink-wave solutions in soft tubes.

Findings

Localized bulging or necking depends on axial stretch.

Super-critical kink-wave solutions occur at a specific threshold.

FEM simulations support theoretical predictions.

Abstract

Previous linear bifurcation analyses have evidenced that an axially stretched soft cylindrical tube may develop an infinite-wavelength (localised) instability when one or both of its lateral surfaces are under sufficient surface tension. Phase transition interpretations have also highlighted that the tube admits a final evolved "two-phase" state. How the localised instability initiates and evolves into the final "two-phase" state is still a matter of contention, and this is the focus of the current study. Through a weakly non-linear analysis conducted for a general material model, the initial sub-critical bifurcation solution is found to be localised bulging or necking depending on whether the axial stretch is greater or less than a certain threshold value. At this threshold value, an exceptionally super-critical kink-wave solution arises in place of localisation. A thorough interpretation of the anticipated post-bifurcation behaviour based on our theoretical results is also given, and this is supported by Finite Element Method (FEM) simulations.