  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.
