We study a prototypical system describing instability effects due to geometric constraints in the framework of nonlinear elasticity. By considering the equilibrium configurations of an elastic ring constrained inside a rigid circle with smaller radius, we analytically determine different possible shapes, reproducing well-known physical phenomena. As we show, both single- (with different complexity) and multi-blister configurations can be observed, but the lowest energy always corresponds to single-blister solutions. Important physical insight is attained through an analogy between the elastica and the dynamics of a nonlinear pendulum. A complete geometric characterization is attained, proving symmetry and other relevant properties. The effectiveness of the model is tested against a simple experiment by considering a thin polymer strip constrained in a rigid cylinder.

中文翻译：

---

几何约束引起的弹性多泡

我们研究了一个原型系统，该系统描述了非线性弹性框架中几何约束引起的不稳定效应。通过考虑约束在半径较小的刚性圆内的弹性环的平衡配置，我们分析确定了不同的可能形状，再现了众所周知的物理现象。正如我们所展示的，可以观察到单（具有不同的复杂性）和多泡罩配置，但最低能量总是对应于单泡罩解决方案。重要的物理洞察力是通过弹性和非线性摆的动力学之间的类比获得的。获得了完整的几何特征，证明了对称性和其他相关属性。