Electromechanical stability of wrinkled dielectric elastomers

Thin dielectric elastomers with compliant electrodes can experience two types of instability: wrinkling, which occurs to relax in-plane compressive stresses through out-of-plane deformations, and electromechanical instability, a sudden thinning deformation that often preludes to dielectric breakdown. In this work we study electromechanical instability of a wrinkled dielectric membrane. The theory, which is based on an averaged description of wrinkles through tension field theory, provides a modification of the so-called “Hessian method” to account for the presence of wrinkles. These findings are consistent with available experimental data, showing that wrinkles in dielectric membranes can be “stable”, in the sense that they can be maintained and restrained, until when electromechanical instability takes place in the wrinkled membrane. We finally provide examples involving both homogeneous and inhomogeneous deformations, showing that the hierarchy of wrinkling and electromechanical instability can be tuned by suitable choices of the electro-mechanical controls.