Electromechanical macroscopic instabilities in soft dielectric elastomer composites with periodic microstructures

We study electromechanical macroscopic instabilities in dielectric elastomer (DE) composites undergoing finite strains in the presence of an electric field. We identify the unstable domains for DE composites with periodically distributed circular and elliptical inclusions embedded in a soft matrix. We analyze the influence of the applied electric field and finite strains, as well as the microstructure geometrical parameters and material properties, on the stability of the DE composites. We find that the unstable domains can be significantly tuned by an electric field, depending on the electric field direction relative to pre-stretch and microstructure. More specifically, the electric field aligned with the stretch direction, promotes instabilities in the composites, and the electric field applied perpendicularly to the stretch direction, stabilizes the composites. Critical stretch decreases with an increase in the volume fraction of circular inclusions. An increase in the contrast between the dielectric properties of the constituents, magnifies the role of the electric field, while an increase in the shear modulus contrast results in a less stable DE composite. For periodic DE composites with elliptical inclusions, we find that the critical stretch depends on the inclination angle of the inclusion, and that the critical stretch reaches a unique maximum at an angle defined by the inclusion ellipticity aspect ratio. In the aligned case - when the longest side of the inclusion is aligned with the stretch direction - an increase in the ellipticity ratio results in an increase in critical stretch.