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

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