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

我们研究在轴向拉伸和表面张力作用下不可压缩的超弹性圆柱管中的局部凸出或颈缩。考虑了三种情况，其中管受到不同的约束。在情况1中，内表面和外表面无牵引力且处于表面张力下，而在情况2和3中，内表面和外表面（分别）是固定的，以防止径向位移和表面张力。但是，在后两种情况下，每个自由表面仍处于表面张力下。我们首先陈述分析的分叉条件以进行局部化，然后通过数值验证它们，同时确定局部化是否比分叉进入周期模式更可取。结果表明，在情况1中分叉到局部解决方案中是不可能的，但在情况2和3中是可能的并且是有利的。在情况1中，任何分叉都必须采用具有非零波数的周期性模式的形式。我们的结果通过有限元方法（FEM）仿真得到了验证。