Green’s functions of a half-infinite piezoelectric body: Exact solutions

Green’s functions of a half-infinite piezoelectric space play an important role in electroelastic analyses of piezoelectric media. However, almost all works available on the topic are based on the assumption that the normal component of the electric displacement is zero on the surface of the piezoelectric solid, neglecting the effect of polarized surface charge. In the present work, we develop an exact solution for the Green’s functions of a half-infinite piezoelectric solid by means of the Stroh formalism. The solution is based on using the exact electric boundary conditions at the interface between the solid and the air medium. First, Green’s function for an arbitrary line load in the solid is derived taking into account the effect of polarized charge at the interface, and then the surface Green’s function for a surface load is obtained as a special example. Finally, by using the superposition principle, a general expression for the polarized charge distribution on the surface of the piezoelectric solid is presented when an arbitrarily distributed force is exerted on the boundary. It is shown that the normal component of the electric displacement on the solid surface is not zero and it is dependent on the applied loads and the electro-elastic constants of the piezoelectric material and air.