Surface instability and pattern formation in two interacting incompressible elastic films bonded to rigid substrates

Abstract

The surface stability of two interacting (for example, by van der Waals or electrostatic forces) incompressible thin elastic films, one bonded to a substrate and the other to a contactor, is studied, extending the work of Shenoy and Sharma (Phys. Rev. Lett. 2001, 18, 119-122), who studied the interaction of a film with a rigid contactor. The surfaces of the films roughen spontaneously when the separation is below a critical value. The linear stability analysis indicates that the wavelength of the instability depends strongly on the shear moduli and thicknesses of the films but not on the nature and magnitude of the interaction. Three cases are considered. First, when the films have equal shear moduli but different thicknesses, the wavelength of the instability has an intermediate value between the wavelengths of the instabilities had each of the films been interacting with rigid contactors. Second, if the films have different shear moduli but equal thicknesses, then the wavelength of the instability (approximately equal to thrice the thickness of the film) is identical to that had the films been interacting with rigid contactors. Third, in the more general case when the two films have different shear moduli and thicknesses, the behavior of the critical wavelength is more complex with several interesting features. For example, when the shear moduli of the films are very different, the critical wavelength depends discontinuously on the ratio of thicknesses of the films. The results of this paper are of interest in understanding contact at soft interfaces, peeling of adhesives, cavitation, and so forth and can stimulate further experiments.