2 research outputs found
Curvature-Induced Instabilities of Shells
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.Comment: 12 pages, 9 figures (including Supporting Information