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  • Open Access

(Dis)continuous buckling transition in elastic shell mediated by contact

Takara Abe

Tomohiko G. Sano*

  • School of Integrated Design Engineering, Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan

  • Department of Mechanical Engineering, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan and School of Integrated Design Engineering, Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan

  • *Contact author: sano@mech.keio.ac.jp
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Phys. Rev. Research 8, 013065 – Published 21 January, 2026

DOI: https://doi.org/10.1103/kph8-2zhf

Abstract

Snap buckling is a rapid shape transition in slender structures, appearing as a fundamental switching mechanism of natural and man-made systems. Boundary conditions of structures are crucial to predict and control their snap buckling behavior. However, the general framework that relates boundary conditions, geometry, and performance of structures is still absent to date. Here, we study the snap buckling of hemispherical shells in contact with rigid cylinders of different diameters to uncover the roles of boundary conditions in dynamic performance of shells. Specifically, we analyze the jumping dynamics of the pneumatically inverted shells placed on the rigid cylinder by combining experiments and analytical theory. We find the characteristic diameter of the cylinder determined from the shell geometry that can switch between continuous and discontinuous buckling associated with the jumping behavior. The analytical predictions for jumping performance of the shell supplemented with the characteristic diameter are in excellent agreement with our experimental results. Our study clarifies that contact geometry is crucial in predicting the pathway of snap buckling, indicating that dynamic performance of soft robots would be optimized by tuning their surface geometry.

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Phys. Rev. Research 8, 013065– Published 21 January, 2026
  • Received 1 April 2025
  • Accepted 31 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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