Voltage-controlled complete stopbands in two-dimensional soft dielectrics

Dielectric elastomers deform and stiffen when subjected to voltage. This work demonstrates how fiber composites made of incompressible dielectric elastomers exhibit complete band gaps-frequency ranges in which elastic wave propagation is prohibited, irrespective of its polarization and direction. To this end, we first analytically determine the quasi-static response of a wide class of composites to an electric field along the fibers. We then formulate and calculate incremental motions of general polarization propagating in the deformed composite, using a plane wave expansion approach. We numerically explore the dependency of the motion on the composite properties and electric field. We show how complete band gaps are tuned by adjusting the electric field, owing to resultant geometrical and physical changes. These results suggest that soft dielectrics can serve as tunable waveguides and filters.