Elasticity, Geometry and Statistics Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev Lett. 2012 Oct 5;109(14):144301. doi: 10.1103/PhysRevLett.109.144301.
We present results from an experimental investigation of the indentation of nonspherical pressurized elastic shells with a positive Gauss curvature. A predictive framework is proposed that rationalizes the dependence of the local rigidity of an indented shell on the curvature in the neighborhood of the locus of indentation, the in-out pressure differential, and the material properties. In our approach, we combine classic theory for spherical shells with recent analytical developments for the pressurized case, and proceed, for the most part, by analogy, guided by our own experiments. By way of example, our results elucidate why an eggshell is significantly stiffer when compressed along its major axis, as compared to doing so along its minor axis. The prominence of geometry in this class of problems points to the relevance and applicability of our findings over a wide range of length scales.
我们展示了对具有正高斯曲率的受压非球形弹性壳的压痕实验研究结果。提出了一个预测框架，该框架使缩进壳的局部刚性对压痕位置附近的曲率、内外压差以及材料特性的依赖性合理化。在我们的方法中，我们将球形壳的经典理论与最近针对受压情况的分析性发展结合起来，并且在大多数情况下，通过类比来进行，以我们自己的实验为指导。例如，我们的结果阐明了为什么与沿着较小轴压缩相比，鸡蛋壳在沿着其长轴压缩时明显更硬。在这一类问题中，几何形状的突出性表明我们的发现具有广泛的适用性和适用性。
