Surface instability of a bilayer elastic film due to surface van der Waals forces

Abstract

The paper studies surface instability of a bilayer elastic film interacting with another flat rigid body through surface van der Waals forces under plane-strain conditions. The analysis is based on an approximate model which reduces the two-dimensional plane-strain problem of the bilayer elastic film to a one-dimensional problem on its surface. The critical value of the interaction coefficient for surface instability and the associated instability mode can be determined easily by identifying the minimum of the interaction coefficient as a function of the wavelength of the instability mode. Among others, the present analysis shows that a stiff bottom layer of a bilayer film can be approximately treated as a rigid substrate only when the surface compliance ratio of the top layer to the bottom layer exceeds a certain critical value. In contrast to a common assumption that nonequal Poisson ratios of the two layers have a minor effect, it is found that different Poisson ratio combinations could have a significant effect on the surface instability of a bilayer elastic film even when the thickness ratio and modulus ratio keep unchanged. In particular, the present study confirms that, unlike a single-layer elastic film which has only one instability mode, a bilayer elastic film can have two distinct surface instability modes when the top layer is more compliant and much thinner than the bottom layer.