Manipulating pressure and shear waves in dielectric elastomers via external electric stimuli

We investigate elastic wave propagation in finitely deformed dielectric elastomers in the presence of an electrostatic field. To analyze the propagation of both longitudinal (P-) and transverse (S-) waves, we utilize compressible material models. We derive explicit expressions for the generalized acoustic tensor and phase velocities of elastic waves for ideal and enriched dielectric elastomer models. We analyze the slowness curves of elastic wave propagation, and find the P-S-mode disentangling phenomenon. In particular, P-and S-waves can be separated by applying an electric field. The divergence angle between P-and S-waves strongly depends on the applied electrostatic excitation. The influence of an electric field depends on the choice of a material model. In the case of the ideal dielectric model, the in-plane shear wave velocity increases with an increase in electric field, while for the enriched model the velocity may decrease depending on material constants. The divergence angle also gradually increases with an increase in electric field, while for the enriched model the angle variation may be limited. Material compressibility affects the P-wave velocity, and for relatively compressible materials the slowness curve of the P-wave evolves from circular to elliptical shape manifesting in an increase in the refraction angle of the P-wave. As a result, the divergence angle decreases with an increase in material compressibility.