Reflection of plane waves from the boundary of an incompressible finitely deformed electroactive half-space

Abstract

Within the framework of the quasi-electrostatic approximation, the theory of the superposition of infinitesimal deformations and electric fields on a finite deformation with an underlying electric field is employed to examine the problem of the reflection of small amplitude homogeneous electroelastic plane waves from the boundary of an incompressible finitely deformed electroactive half-space. The theory is applied to the case of two-dimensional incremental motions and electric fields with an underlying biassing electric field normal to the half-space boundary, and the general incremental governing equations are obtained for this specialization. For illustration, the equations are then applied to a simple prototype electroelastic model for which it is found that only a single reflected wave is possible and a surface wave is in general generated for each angle of incidence. Explicit formulas are obtained for the wave speed and the reflection and surface wave coefficients in terms of the deformation, magnitude of the electric (displacement) field, the electromechanical coupling parameters, and the angle of incidence, and the results are illustrated graphically.