圆管中生长诱导的水泡
Growth-induced blisters in a circular tube
摘要：
附着在约束基底上的弹性膜的生长可能导致形成定界气泡。当衬底是平坦的时，已经导出了许多结果。平衡形状，超越小的变形，是由片材弹性能量和由于毛细作用的粘附力之间的相互作用决定的。在这里，我们研究了一个非平凡的概括这个问题，并考虑一个不断增长的弹性环的约束\emph{circular}基板的粘附。基本方程，即，用变分法导出了欧拉方程、边界条件和横截性条件。与平面情况相反，界定壁的曲率出现在横向条件下，因此充当另一个粘附源。我们提供的分析解决方案，研究中的问题，在椭圆积分和执行的数值和渐近分析的特征长度的水泡。最后，与以往的研究相比，我们还讨论了力学和内部应力的情况下，消失的粘附。具体来说，我们对在小余长极限下观察到的条带施加在容器上的平均压力的发散给出了理论解释。
英文摘要：
The growth of an elastic film adhered to a confining substrate might lead to the formation of delimitation blisters. Many results have been derived when the substrate is flat. The equilibrium shapes, beyond small deformations, are determined by the interplay between the sheet elastic energy and the adhesive potential due to capillarity. Here, we study a non-trivial generalization to this problem and consider the adhesion of a growing elastic loop to a confining \emph{circular} substrate. The fundamental equations, i.e., the Euler Elastica equation, the boundary conditions and the transversality condition, are derived from a variational procedure. In contrast to the planar case, the curvature of the delimiting wall appears in the transversality condition, thus acting as a further source of adhesion. We provide the analytic solution to the problem under study in terms of elliptic integrals and perform the numerical and the asymptotic analysis of the characteristic lengths of the blister. Finally, and in contrast to previous studies, we also discuss the mechanics and the internal stresses in the case of vanishing adhesion. Specifically, we give a theoretical explanation to the observed divergence of the mean pressure exerted by the strip on the container in the limit of small excess-length.
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