Instability of compressible soft electroactive plates

In this paper, we investigate the formation of two-dimensional surface wrinkles in a pre-deformed compressible soft electroactive (SEA) plate. Two common electrical loading protocols are considered: one is the so-called voltage-control where the plate is applied with a constant voltage across the thickness; the other is named as charge-control where the plate is activated by uniformly spraying electrical charges on its main faces. By developing the surface impedance matrix method with the Stroh formulation for compressible SEA materials, we decouple the resulting dispersion equations into symmetric and antisymmetric modes and obtain the associated closed-form expressions, respectively. These analytical expressions of the critical stretch are crucial to the quantitative understanding of wrinkling in the SEA plate. For illustration, we treat examples of compressible Gent and neo-Hookean ideal dielectric elastomers. Results show that the symmetric wrinkles may appear prior to the antisymmetric ones in a sufficiently stretched compressible SEA plate. This phenomenon is in principle caused by the release of incompressibility constraint, upon which the variation of the material chain extension limit only mildly affects the magnitude of the critical stretch. Especially, for charge-controlled plates, a compressibility-driven competition mechanism is revealed that with the increase of compressibility, the symmetric wrinkling is promoted while the antisymmetric one is suppressed. Moreover, enhancing compressibility significantly stabilizes the intrinsic instability of charge-controlled plate while makes the voltage-controlled plate more unstable. These findings, for the first time, systematically demonstrate the great significance of material compressibility on the nonlinear response and stability performance of SEA elastomers and can serve a quantitative guidance for the industrial design of new-generation SEA-based devices by exploring the material compressibility.