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Sliding of a cylindrical shell into a rigid hole
Yukiho Matsumoto1, Keisuke Yoshida2, Tomohiko G Sano1,3
1Keio University, School of Integrated Design Engineering, Graduate School of Science and Technology, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan.
Physical Review. E
|April 18, 2026
Summary
This study presents a predictive model for snap-fit assembly, analyzing the mechanics of a curved beam in a rigid hole. It identifies three sliding modes (folding, pinning, unfolding) crucial for designing elastic and rigid structures.
Area of Science:
- Mechanical Engineering
- Materials Science
- Physics
Background:
- Snap-fit joints are common in manufacturing complex structures, involving flexible and rigid components.
- Current snap-fit design heavily relies on empirical rules and prototyping.
- Understanding the mechanics of elasticity, geometry, and friction is key to snap-fit assembly.
Purpose of the Study:
- To develop an analytical model for snap-fit assembly involving a naturally curved beam and a rigid hole.
- To investigate the influence of elasticity, geometry, and contact friction on snap-fit mechanics.
- To provide a predictive framework for designing structures with elastic and rigid components.
Main Methods:
- Constructed an analytical model based on the theory of elastica with contact friction.
- Validated the model using simulations and experimental data.
- Analyzed the sliding behavior of the beam within the rigid hole.
Main Results:
- The analytical model showed excellent quantitative agreement with simulations and experiments.
- Identified three distinct sliding modes: folding, pinning, and unfolding.
- Developed a phase diagram to classify these modes based on geometric parameters.
Conclusions:
- The study offers a predictive framework for snap-fit structures incorporating friction, elasticity, and geometry.
- Provides a unified understanding of interactions between elastic and rigid bodies in contact.
- Advances snap-fit design beyond empirical methods towards a physics-based approach.
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