Non-local elastic effects in electroactive polymers

• We study the onset of inhomogeneous configurations in electroactive polymers.
• A special variational formulation is adopted to describe charge localization effects.
• Non-local elastic effects are considered in the constitutive response of the polymer.
• It is found that localization effects can drastically reduce the pull-in thresholds.
• Both unbounded and bounded length have been considered for the bifurcation analysis.

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.