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We investigate localised bulging or necking in an incompressible,hyperelastic cylindrical tube under axial stretching and surface tension. Threecases are considered in which the tube is subjected to different constraints.In case 1 the inner and outer surfaces are traction-free and under surfacetension, whilst in cases 2 and 3 the inner and outer surfaces (respectively)are fixed to prevent radial displacement and surface tension. However, eachfree surface in these latter two cases is still under surface tension. We firststate the analytical bifurcation conditions for localisation and then validatethem numerically whilst determining whether localisation is preferred overbifurcation into periodic modes. It is shown that bifurcation into a localisedsolution is unattainable in case 1 but possible and favourable in cases 2 and3. In contrast, in case 1 any bifurcation must necessarily take the form of aperiodic mode with a non-zero wave number. Our results are validated usingFinite Element Method (FEM) simulations.

Localised bifurcation in soft cylindrical tubes under axial stretching and surface tension