实验技术与管理

表面张力引起的结构屈曲在圆形截面构件中广泛存在，但后屈曲阶段复杂形态的形成机理尚缺乏统一解释。文章通过实验观测、机器学习分类、数值仿真与三维图形重建技术，系统研究了液体肥皂表面张力作用下聚合物圆环的后屈曲变形行为。实验发现，随着圆环半径的增加，聚合物圆环的结构形态依次经历圆形、椭圆、“8”字形及长接触线“8”字形的连续演化，并伴随显著的面外弯曲。支持向量机分类结果验证了初始屈曲条件与经典Timoshenko理论的预测一致；数值仿真成功复现了实验现象，三维重建模型进一步计算了系统总能量，发现变形后构型的总能量始终低于未变形状态，且随半径增加基本稳定在近似恒定的低能量水平。结果表明：初始屈曲完成了主要的能量释放，使系统进入能量低谷，后续复杂形态演化是系统在维持最低能量水平的前提下，通过局部趋近圆形截面的自适应策略来容纳不断增加的结构周长。研究为圆形截面构件后屈曲行为的实验研究提供了新的分析思路，对海洋工程、航空航天及生物医学等领域的抗屈曲设计具有参考价值。

[Objective] Surface tension can induce instability in slender ring structures， leading to complex post-buckling configurations; however， the mechanism underlying the evolution of these configurations， along with their energy characteristics， is not fully understood. This study investigates the deformation behavior of polymer rings under surface tension and clarifies the energy-driven mechanism underlying post-buckling evolution. [Methods] Polymer rings with rectangular cross-sections were fabricated using polyethylene terephthalate rods， and double-layer soap films were applied to generate uniform surface tension loading. The deformation process was recorded using a high-resolution imaging system， and geometric parameters， including the ring radius and cross-sectional properties， were extracted from the experimental images. A support vector machine model was established to classify the buckling states based on these parameters. Finite element simulations were performed using Abaqus to reproduce the deformation process and analyze the stress and deformation distributions. A three-dimensional reconstruction method based on image processing was also employed to obtain the spatial configurations of the post-buckled shapes. The total energy of the system was calculated by combining the bending strain energy， which was obtained through curvature integration along the ring centerline， and the interfacial energy， which was simplified using Young’s equation. The contact areas between the solid， liquid， and air phases were extracted from the experimental images and the simulation results. [Results] The results show that the ring undergoes a sequence of morphological transitions with increasing radius. The shape evolves from a circular configuration to an elliptical configuration， then to a figure-eight configuration， and finally to a configuration with extended contact regions， accompanied by substantial out-of-plane deformation. The support vector machine classification results agree well with the theoretical predictions of the critical buckling condition， and the finite element results are consistent with the experimental observations in overall morphology and deformation trends. Energy analysis indicates that the total energy of the deformed configuration is lower than that of the initial circular configuration， with the largest reduction occurring at the onset of buckling. Thereafter， the total energy remains relatively stable with increasing radius. The curvature distribution of the complex configurations shows that local segments tend to approach circular arcs， thereby reducing the bending energy， and the introduction of out-of-plane deformation further decreases the system energy. [Conclusions] The post-buckling behavior of polymer rings is governed by energy minimization under surface tension. Buckling leads to a substantial reduction in system energy， and subsequent deformation maintains this low-energy state. Complex configurations are formed through local curvature adjustment and three-dimensional deformation. The proposed experimental and numerical methods provide an effective approach for analyzing surface tension–induced instability， and the results provide a reference for the design of flexible structures and anti-buckling systems in engineering applications.