Stability of a thin elastic film interacting with a contactor

Abstract

The surface stability of a thin solid elastic film subjected to surface interactions such as van der Waals forces due to the influence of another contacting solid is investigated. It is found that for nearly incompressible soft (shear modulus less than 10 MPa) films, the film surface is unstable and forms an undulating pattern without any concurrent mass transport. A complete stability/bifurcation diagram is obtained. A key new result uncovered in this analysis is that the characteristic wavelength of the bifurcation pattern is nearly independent of the precise nature and magnitude of the interaction and varies linearly with the film thickness, whenever the force of interaction attains a critical value. The rate of growth of perturbations is also analysed using a viscoelastic model and it is found that in nearly incompressible materials, the wavelength of the fastest growing perturbation is identical to that of the critical elastic bifurcation mode. These results provide a quantitative explanation for recent experiments. The present study is important in understanding problems ranging from adhesion and friction at soft solid interfaces, peeling of adhesives to the development of micro-scale pattern transfer technologies.