论文标题
带有固定末端的充气橡胶管的局部膨胀
Localised bulging of an inflated rubber tube with fixed ends
论文作者
论文摘要
当在体积控制下膨胀具有游离末端的橡胶管时，压力将首先达到最大值，然后单调地减小以接近恒定渐近线。压力最大对应于局部凸起的启动，并通过分叉条件预测，而渐近线是对应于“两相”传播状态的麦克斯韦压力。相比之下，当试管首先预先伸展并在随后的通货膨胀期间固定末端时，压力与凸起幅度既具有最大和最小值），并且右上升支的行为以前尚未完全理解。我们表明，对于所有伸展和管长度的值，上升分支都收敛到单曲线，仅取决于管子厚度与外半径的比率。该曲线代表在每种情况下要接近的麦克斯韦状态（如果Euler屈曲或轴对称皱纹不会首先发生），但是与自由端情况相比，该状态与压力有关。我们还通过实验证明，当伸直前足够大并研究哪些应变功能可以预测这种观察到的现象时，就不会发生局部凸起。
When a rubber tube with free ends is inflated under volume control, the pressure will first reach a maximum and then decrease monotonically to approach a constant asymptote. The pressure maximum corresponds to the initiation of a localised bulge and is predicted by a bifurcation condition, whereas the asymptote is the Maxwell pressure corresponding to a "two-phase" propagation state. In contrast, when the tube is first pre-stretched and then has its ends fixed during subsequent inflation, the pressure versus bulge amplitude has both a maximum and a minimum, and the behaviour on the right ascending branch has previously not been fully understood. We show that for all values of pre-stretch and tube length, the ascending branches all converge to a single curve that is only dependent on the ratio of tube thickness to the outer radius. This curve represents the Maxwell state to be approached in each case (if Euler buckling or axisymmetric wrinkling does not occur first), but this state is pressure-dependent in contrast with the free-ends case. We also demonstrate experimentally that localized bulging cannot occur when the pre-stretch is sufficiently large and investigate what strain-energy functions can predict this observed phenomenon.
