Non-local elastic effects in electroactive polymers

In this work we study the onset of inhomogeneous deformations in thin electroactive polymers (EAPs) under voltage control. In order to account for the regularizing effects due to both the constitutive nature of the film and to its mechanical interaction with the compliant electrodes, we introduce a non-local energy term depending on the second gradient of deformation. We prove that very small non-local effects are sufficient to find realistic inhomogeneous deformations at the onset of the bifurcation, which are characterized by periodic thickness undulations with finite wavelength. Finally we prove that strong regularizing effects can suppress the onset of inhomogeneous deformations.