Inhomogeneous thinning of imperfect dielectric elastomer films: Large deformation and nonlinear electromechanical instability

Abstract

In this paper, we study the inhomogeneous thinning of a circular dielectric film with a concentric hole subjected to electromechanical loads. The effects of the hole size on the inhomogeneous thinning, the electro-cavitation and pull-in instability of soft dielectric films are seldom investigated. To clarify the highly nonlinear electromechanical behavior, we obtain a two-point boundary-value problem that is first reported in the thinning of dielectric films. The formulation can capture the electromechanical behaviors of soft dielectric films with and without a hole. In the latter case, our numerical predictions match exactly with the well-known analytical results. We carry out our analysis by using neo-Hookean dielectrics and find that there is no electro-cavitation in incompressible dielectric films subjected to electromechanical loads. It is interesting that pull-in instability and the inhomogeneous thinning depend on the hole size only if the mechanical load is nonzero. The hole size decreases either the critical electric field or the mechanical load for the onset of pull-in instability. This paper is desirable to further the understanding of large deformation and failure mechanism of imperfect dielectric films.