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Buckling dynamics of elastic shells

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Buckling of elastic structures has recently emerged as a powerful mechanism for triggering rapid small-scale motion. This concerns the rapid reorientation of microswimmers, the generation of propulsion, the actuation of valves for flow control or the rapid focusing of optical lenses. The dedicated design of complex materials to achieve the desired buckling behavior has become an intense field of research in recent years. While stable configurations of flexible structures subject to buckling have been widely explored, their complete control by external signals requires a better understanding of their dynamics. Due to their simple fabrication, hollow spherical shells are among the most studied objects. Under pressure, they collapse into a bowl shape.

Through experiments on centimeter-sized elastomeric shells and 3D numerical simulations, the research team studied the dynamics of these shells at the beginning of the buckling process and during their post-buckling oscillations.
For the first stage of the buckling process, experiments were conducted with shells of different thicknesses, on which a sudden overpressure was applied to induce buckling. Through a collaboration with Douglas Holmes’ group at Boston University, USA, the resulting dynamics were understood by modeling the process as the growth of the defect where the buckling was initiated.
In a second study conducted in collaboration with Sebastian Aland’s group in Freiberg, Germany, the researchers determined how the shell oscillates in its bowl-shaped geometry. They found that it does so at a much lower frequency than in the spherical configuration. In contrast to previous empirical models, they showed that this low frequency can be associated with variations in the surface area of the shell at constant volume. They developed a theoretical model describing the observed bi-harmonic oscillations, which could be used in the future to better understand the nonlinear coupling between shells and pressure waves.

In particular, such encapsulated bubbles are commonly used by sonographers to improve image contrast after being injected into blood vessels. The results will provide a better understanding of the ultrasound signals emitted by these bubbles when excited by high amplitude ultrasound.

These results were published in two simultaneous papers in Proceeedings of the Royal Society A:

- Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load
Lucia Stein-Montalvo, Douglas P. Holmes and Gwennou Coupier
Proc. R. Soc. A (2021). (doi:10.1098/rspa.2021.0253)

- Post-buckling Dynamics of Spherical Shells
Marcel Mokbel, Adel Djellouli, Catherine Quilliet, Sebastian Aland and Gwennou Coupier
Proc. R. Soc. A (2021). (doi:10.1098/rspa.2021.0378)

Contact: Gwennou Coupier