Curvature-Induced Instabilities of Shells

Abstract

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains still poorly understood. Via a combination of precision experiments on elastomeric spherical bilayer shells, simulations, and theory, we show a spontaneous curvature-induced rotational symmetry-breaking as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities and their dependence on geometry are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike bulk term and a torquelike boundary term, allowing scaling predictions for the instabilities in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.

arXiv comment12 pages, 9 figures (including Supporting Information)

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• Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: a macroscopic analog of thermodynamic phase transition
• The nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature
• Let's deflate that beach ball
• Post-buckling Dynamics of Spherical Shells
• Fluid-induced snap-through instability of spherical shells