Surface wrinkling of two mutually attracting elastic thin films due to van der Waals forces

Abstract

This article studies surface instability of two mutually attracting elastic films due to van der Waals forces under plane strain conditions. The analysis is based on an approximate method which reduces a two-dimensional problem of an elastic film to a one-dimensional surface problem. This method is much simpler than the conventional method and allows one to easily identify the critical value of the interaction coefficient and the surface instability mode. The accuracy of this method is demonstrated by the excellent agreement (with relative errors less than 5%) between the predicted results and the known exact data for a special case of an elastic film interacting with a rigid flat surface. The incompatibility of the individual fundamental modes of two elastic layers with unequal thickness results in two distinct metastable instability modes when the thickness ratio exceeds a critical value, in contrast to the uniqueness of the surface instability mode of an elastic film attracted to a rigid flat surface. This nonuniqueness of the metastable instability modes would cause complex surface instability phenomena of two interacting elastic films (such as jump between the two instability modes).