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

Fu

Abstract

Previous linear bifurcation analyses have evidenced that an axially stretched soft cylindrical tube may develop an infinite-wavelength (localized) 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 localized 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 nonlinear analysis conducted for a general material model, the initial sub-critical bifurcation solution is found to be localized 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 localization. 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 simulations.

Citation

Fu. (2021). Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1-21. https://doi.org/10.1098/rspa.2021.0311

• Acceptance Date: Sep 9, 2021
• Publication Date: Oct 27, 2021
• Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-5021
• Publisher: The Royal Society
• Pages: 1-21
• DOI: https://doi.org/10.1098/rspa.2021.0311
• Publisher URL: https://royalsocietypublishing.org/doi/10.1098/rspa.2021.0311