Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA.
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev Lett. 2018 Jan 26;120(4):048002. doi: 10.1103/PhysRevLett.120.048002.
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 poorly understood. Via a combination of precision experiments on elastomeric spherical shells, simulations, and theory, we show how a spontaneous curvature induces a rotational symmetry-breaking buckling 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 term in the bulk and a torquelike term in the boundary, allowing scaling predictions for the instabilities that are in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced subcritical 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.
在细胞膜内的蛋白质或差异生长、加热或膨胀的诱导下，自发曲率会极大地影响薄体的形态，并引发机械不稳定性。然而，曲面壳中的自发曲率和几何约束之间的相互作用仍未得到很好的理解。通过对弹性球壳的精密实验、模拟和理论的结合，我们展示了自发曲率如何诱导旋转对称破缺的屈曲以及类似于捕蝇草闭合机制的快速不稳定性。通过将自发曲率简化为有效的机械载荷，我们可以对不稳定性及其对几何形状的依赖性进行合理化解释。这种表述在体相中产生了类似于压力的项，在边界上产生了类似于扭矩的项，从而可以对不稳定性进行标度预测，其结果与实验和模拟非常吻合。此外，有效压力类比表明在封闭壳中存在曲率诱导的亚临界屈曲。我们通过考虑残余膜和弯曲应力的组合的线性稳定性分析来确定临界屈曲曲率。我们的发现中几何形状的突出作用表明这些结果在广泛的尺度上具有适用性。
