Department of Engineering, University of Cambridge, Trumpington St., Cambridge CB2 1PZ, UK.
Soft Matter. 2018 Sep 26;14(37):7680-7689. doi: 10.1039/c8sm01033a.
We consider meniscus instabilities in thin elastic layers perfectly adhered to, and confined between, much stiffer bodies. When the free boundary associated with the meniscus of the elastic layer recedes into the layer, for example by pulling the stiffer bodies apart or injecting air between them, then the meniscus will eventually undergo a purely elastic instability in which fingers of air invade the layer. Here we show that the form of this instability is identical in a range of different loading conditions, provided only that the thickness of the meniscus, a, is small compared to the in-plane dimensions and to two emergent in-plane length scales that arise if the substrate is soft or if the layer is compressible. In all such situations, we predict that the instability will occur when the meniscus has receded by approximately 1.27a, and that the instability will have wavelength λ ≈ 2.75a. We illustrate this by also calculating the threshold for fingering in a thin wedge of elastic material bonded to two rigid plates that are pried apart, and the threshold for fingering when a flexible plate is peeled from an elastic layer that glues the plate to a rigid substrate.
我们研究了完全附着在更硬的两个物体之间的弹性层中的半月板不稳定。例如，当与弹性层的半月板相关的自由边界退缩到层中时，例如通过拉开更硬的物体或在它们之间注入空气，那么半月板最终将经历纯粹的弹性不稳定性，其中空气的指状物侵入层中。在这里，我们表明，在各种不同的加载条件下，这种不稳定性的形式是相同的，只要半月板的厚度 a 与平面内尺寸以及如果基底较软或如果层可压缩，则出现的两个平面内长度尺度相比都很小。在所有这些情况下，我们预测当半月板后退约 1.27a 时，不稳定性将发生，并且不稳定性将具有波长 λ≈2.75a。我们通过计算也说明了这一点，计算了与两个刚性板分离的两个刚性板结合的薄楔形弹性材料中的指状物的阈值，以及从将板粘合到刚性基板的弹性层剥离的柔性板的指状物的阈值。
