Mindlin's problem for an anisotropic piezoelectric half-space with general boundary conditions

This paper considers Mindlin's problem in an anisotropic and piezoelectric half-space with general boundary conditions, including 16 different sets of surface conditions. The Green's function due to a point force or point electric charge within the half-space, also called the generalized Mindlin problem, is solved. Based on the extended Stroh formalism and two-dimensional Fourier transforms in combination with Mindlin's superposition method, the generalized Mindlin solution is expressed as a sum of the generalized Kelvin solution and a complementary part. While the full-space Green's function is in an explicit form, the complementary part is expressed in terms of a simple line integral over [0, pi]. Of the 16 different sets, detailed studies are presented for the four common surface conditions, i.e. the traction-free insulating and conducting, and rigid insulating and conducting surface conditions. With the exception of the solution to the traction-free insulating boundary condition, solutions to the other sets of boundary conditions are new. Furthermore, the corresponding two-dimensional solutions are also derived analytically for the 16 different sets of boundary conditions for possibly the first time. Numerical examples of the generalized Mindlin solution are carried out for two typical piezoelectric materials, one being quartz and the other ceramic, with the four common surface conditions. These numerical results illustrate clearly the significance of different boundary conditions as well as the electromechanical coupling in the Mindlin's problem analysis.