Tunable permittivity in dielectric elastomer composites under finite strains: Periodicity, randomness, and instabilities.

We study the interplay between the material composition and deformation in dielectric elastomer (DE) composites with periodically and randomly distributed particles embedded in a soft matrix. We focus on the deformation-induced tunability of the effective permittivity in DE composites. We examine the effects of microstructural periodicity and its transition towards random distribution. In particular, we analyze the DE composites with periodic microstructures of (a) circular and (b) elliptical inclusions, (c) pair of inclusions, and (d) randomly distributed inclusions with different numbers of the particles in the unit cell. The finitely deformed DE composites with ideal dielectric elastomer constituents are analyzed numerically. In addition, for the periodic DE composites with circular inclusions, we derive an explicit relation between the effective permittivity and stretch. The effective permittivity of DE composites with periodic microstructures changes with deformation, whereas in DE composites with randomly distributed inclusions, the permittivity is barely affected by deformation. For the latter case, the effective permittivity attains a certain value as the number of particles in the periodic cell increases. To provide the insights on the composite behavior, a two-particle periodic system is examined. The permittivity is found to be sensitive to the orientation of the pairs with respect to the applied electric field, and the distance between the particles. The geometrical effects amplify significantly as the inter-particle distance becomes less than their two diameters. Finally, we illustrate the permittivity tunability in DE periodic porous composites structures experiencing elastic instabilities.