Electrostatically tunable band gaps in finitely extensible dielectric elastomer fiber composites

The structure of band-gaps in actuated fiber-reinforced dielectric elastomer composites with square lattice is studied. The constitutive behaviors of the phases are characterized by an augmented Gent strain energy density function, to account for the strain-hardening of the elastomer. The finite static deformation of the composite is calculated when subjected to an electric bias field along the fibers. The anti-plane mode of small electroelastic waves propagating in the material deformed configuration is determined by means of a proper adjustment of the plane-wave expansion method. The resultant eigenvalue problem supplies the dispersion relation from which bands of prohibited frequencies are determined. The band structures of exemplary composites with circular fibers are evaluated for various values of the bias electric field. The dependency on the properties and volume fractions of the phases, and most importantly the bias electric field is explored. It is revealed how enhancing the intensity of the electrostatic field widens the bands and shifts them toward higher frequencies. These results suggest the use of dielectric elastomer composites as control mechanisms for electroelastic wave propagation by properly tuning the electrostatic excitation.