Laboratoire Matière et Systèmes Complexes

Snap-buckling driven by boundary conditions

Dr. Tomohiko Sano

JSPS Overseas Research Fellow Flexible Structures Laboratory, Institute of Mechanical Engineering, École polytechnique fédérale de Lausanne, Switzerland

Abstract : Slender structures span more than ten orders of magnitude in length scale ; examples include from submarine cables, climbing ropes, gift-wrapping ribbons, plant tendrils, to micro-scales, membranes, flagella and cilia. Slender structures deform largely by a small load, while their strain is small. This fact reminds us that geometry, such as curvature and twist, and mechanics are inseparable (Fig. 1). Because the deformation of slender structures rely primarily on geometric nonlinearities, studies of specific structures would provide common knowledge in seemingly different physical phenomena.

Fig. 1 Large deformation of a thin elastic ribbon.

In this seminar, we focus on dynamic functionality in slender structures known as snap-buckling. When a beam is subjected to axial compressive stress, it bends and buckles in either upward or downward direction. By indenting the peak of the bent beam (keeping the amount of compressive stress), the beam snaps to switch the buckling direction. Snap-buckling is the ubiquitous switching or (athermal) transition phenomena in slender structures. Snap-buckling plays important roles not only in switching devices but also in fast phenomena in plants, such as seed dispersal or carnivorous plants. Combining experiments and theory, we discuss novel snapping behaviours, purely controlled by boundary conditions, in elastic ribbons and strips (Fig. 2)[1,2].

Fig. 2 Twist-induced snap-buckling in a bent elastic ribbon

Refs. [1] T. G. Sano and H. Wada, Phys. Rev. E 97, 013002 (2018). [2] T. G. Sano and H. Wada, Phys. Rev. Lett 122, 114301 (2019).