Electroelastic waves in a finitely deformed electroactive material

In this paper, the coupling between a finite deformation and an electric field is examined with particular reference to the propagation of small amplitude waves in a non-linear electroelastic material based on the quasi-electrostatic approximation. The general equations governing the linearized response of electroelastic solids superimposed on a state of finite deformation in the presence of an electric field are derived along with incremental forms of the electroelastic constitutive laws and boundary conditions. Both unconstrained and incompressible materials are considered. Without restriction on the electroelastic constitutive law, the theory is first applied to the analysis of plane waves propagating in a homogeneously deformed material with an underlying uniform electric field and illustrated in the case of an isotropic material. The general equations governing 2D incremental motions are then derived and applied to the study of surface waves in a homogeneously deformed half-space of incompressible isotropic material with the electric field normal to the surface of the half-space. The dependence of the wave speed on the deformation, the electric field and the electromechanical coupling parameters is illustrated for a prototype electroelastic constitutive law.