Electro-mechanical surface wrinkling of a finite block of dielectric elastomers accounting for the pre-stretch and the aspect ratio

Surface instability of elastomers is of great interest in engineering science, especially in the characterization of flexible electronic materials and the manufacture of micro-nano surface topography. There is limited research on how the geometry of the block affects wrinkle appearance in a multiphysics environment. In this paper, we formulate the boundary-value problem and its incremental forms to analyze the sinusoidal surface instability of a neo-Hookean dielectric block subjected to electromechanical loads. We discover that the competition between the Maxwell stress, induced by the voltage, and the mechanical stress caused by the stretch, plays a crucial role in inducing surface wrinkling. Furthermore, we find that the aspect ratio of the block can modify the critical value of the combination of voltage and pre-stretch required for wrinkling. In addition to this, the aspect ratio also affects the shape of the wrinkling. Specifically, if the elastomer block has a smaller aspect ratio, its sinusoidal wrinkling will have a larger wavenumber. Our paper enhances the understanding of surface instability in electrostrictive elastomers and provides guidance on triggering it without breaking down the elastomer.