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.

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.

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.

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.

As global trade integration accelerates, the frequency of transnational cargo transportation has surged, spotlighting the development of railways as a crucial objective for various countries. Railways offer the advantages of low cost and high transportation capacity. However, the efficiency of goods transportation is hampered by the disparities in track gauges between countries. Among the numerous proposed solutions, the variable gauge bogie can efficiently solve this problem. However, in practical applications, micro-fretting wear between wheels and axles of variable gauge vehicles can lead to connection relaxation and failure, posing potential safety hazards. Although experimental results have demonstrated that surface treatment technology can effectively reduce friction and wear between wheels and axles, the underlying micro-wear reduction mechanism remains poorly understood.

This study uses the molecular dynamics method to develop a three-dimensional micro-fretting wear model for bogie wheels and axles. This study aims to elucidate the wear reduction mechanism of surface treatment technology from a microscopic perspective and provides experimental validation. The micro-canonical ensemble, also known as the NVE ensemble, was selected to stimulate the working conditions between the wheel and axle, ensuring that the system was isolated from external energy and particle exchanges. The embedded atom model is suitable for intermetallic molecular dynamics simulation. In this study, EAM was used for relaxation processing to accurately characterize the interactions between atoms within the alloy in a stable state. Meanwhile, the Lennard-Jones (LJ) potential, known for its simple structure and computational efficiency, was applied to calculate the interaction force between the wheel and axle interfaces with high precision. Therefore, the LJ potential plays a crucial role in the present study, representing the complex interface interactions.

The results show that under contact stress, a slight protrusion contact occurs between the two surfaces of the wheel axle, leading to deformation and adhesion. When these surfaces are separated, the adhesion material from the protrusions is detached by shear force, causing micro-motion wear. To explore solutions, two molecular dynamics models of surface treatment processes were developed: one involving coating with MoS₂ and the other ion nitriding. The calculations reveal that both surface treatment processes significantly reduce wear, as evidenced by a lower average friction coefficient. Further analysis of the temporal variation in lateral and longitudinal forces uncovers that the wear reduction effect of these surface treatment processes stems primarily from a decrease in lateral force. In addition, it was found that the friction coefficient of the MoS₂ coating model decreases with an increasing load. Conversely, the friction coefficient of the ion nitriding model decreases with an increased amount of nitriding. To ensure the accuracy of these simulation results, experiments were conducted using the WTM-2E controllable atmosphere micro friction and wear tester.

Experimental and simulation results demonstrate that MoS₂ coating and ion nitriding treatments effectively enhance lubrication and reduce wear. These treatments improve the processing performance of components, extend their service life, and minimize potential safety hazards. The application of molecular dynamics simulation in analyzing micro-motion wear offers significant educational value, particularly in the context of courses on Friction Wear and Lubrication. It provides students with a tangible understanding of how micro-motion affects the macroscopic performance of materials and components.