Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA.
Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev Lett. 2014 Mar 7;112(9):094302. doi: 10.1103/PhysRevLett.112.094302. Epub 2014 Mar 6.
The formation of localized periodic structures in the deformation of elastic shells is well documented and is a familiar first stage in the crushing of a spherical shell such as a ping-pong ball. While spherical shells manifest such periodic structures as polygons, we present a new instability that is observed in the indentation of a highly ellipsoidal shell by a horizontal plate. Above a critical indentation depth, the plate loses contact with the shell in a series of well-defined "blisters" along the long axis of the ellipsoid. We characterize the onset of this instability and explain it using scaling arguments, numerical simulations, and experiments. We also characterize the properties of the blistering pattern by showing how the number of blisters and their size depend on both the geometrical properties of the shell and the indentation but not on the shell's elastic modulus. This blistering instability may be used to determine the thickness of highly ellipsoidal shells simply by squashing them between two plates.
弹性壳变形中局部周期结构的形成已有大量记载，这是乒乓球等球形壳压碎的常见初始阶段。虽然球形壳表现为多边形等周期性结构，但我们提出了一种新的不稳定性，这种不稳定性存在于水平板压入高度各向异性壳时。在临界压入深度以上，板在沿着长轴的一系列明确定义的“气泡”中与壳失去接触。我们用标度分析、数值模拟和实验来描述这种不稳定性的发生，并解释其原因。我们还通过显示气泡的数量及其大小如何取决于壳的几何形状和压入深度，而不取决于壳的弹性模量，来描述气泡模式的特性。这种起泡不稳定性可用于通过在两个板之间挤压高度各向异性壳来确定其厚度。
