Stability of a Thin Solid Film with Interactions

We investigate the question of stability of a solid thin film which experiences external interactions such as van der Waals forces from a contacting surface or forces from an external electric field. Both perfectly elastic and viscoelastic material behaviours are considered in linear stability analysis performed here. These analyses indicate that for sufficiently soft (shear modulus between 1 and 10 MPa) and nearly incompressible films (Poisson's ratio close to 0.5), bifurcations are possible, i.e., the surface of the film becomes non-planar. The modes of bifurcation and rates of growth of perturbations are determined as a function of material parameters. The results of this study are of significance in understanding the adhesive properties between a soft material (such as rubber) and a comparatively rigid solid (such as steel), and the behaviour of soft solid films in an electric field.