On the Green’s functions for a two-phase soft electroactive medium subjected to biasing fields

We consider the problem of a point force and/or a point charge applied in the interior of an infinite two-phase medium, which consists of two perfectly or smoothly bonded soft electroactive half-spaces. Both two half-spaces are initially subjected to an arbitrary multi-directional stretch and a biasing electric field. A linearized incremental theory is adopted to describe the deformation caused by the point force and/or point charge. A concise general solution to the governing equations of the perturbed infinitesimal elastic and electric fields is employed. By the trial-and-error method, the analytical expressions for the quasi-harmonic functions in the general solution are constructed explicitly, but with several undetermined constants. These constants can be easily determined from the conditions on the perfect or smooth interface as well as some other considerations. As special cases of the present two-phase Green’s functions, the generalized Mindlin solution and Lorentz solution for an electroactive half-space subjected to an initial biasing field are discussed. The more specified generalized Boussinesq solution and Cerruti solution are also given in the appendix.