Functionally Graded Soft Dielectric Elastomer Phononic Crystals: Finite Deformation, Electro-Elastic Longitudinal Waves, and Band Gaps Tunability via Electro-Mechanical Loading

Active tuning of elastic wave band gaps received significant attention in the recent past. To this end, soft dielectric elastomers (DEs) have indicated great promise owing to their capability to undergo large reversible deformations and deformation-dependent constitutive properties. In this paper, we investigate the longitudinal wave band gaps an infinite periodic soft functionally graded dielectric elastomer subjected to electro-mechanical biasing fields. Material properties of the functionally graded DE are described by the power law. The nonlinear hyperelastic compressible neo–Hookean model is employed for characterizing the constitutive behavior of the soft functionally graded dielectric elastomer. The finite element method with Bloch–Floquet theory is employed for finding the band-structure of the infinitely periodic soft functionally graded DE structure. A parametric study brings out the effect of biasing fields and power law exponent on the band gap characteristics. The biasing mechanical prestress, the electric displacement field show significant influence on position and the width of band gaps. The inferences reported here can find their potential use in the design of soft DE wave devices with tunable band structures.