The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials

Firstly, the extended Boussinesq and Cerruti solutions for point forces and point charge acting on the surface of a transversely isotropic piezoelectric half-space are derived. Secondly, aiming at a series of common three-dimensional contact including spherical contact, a conical indentor and an upright circular ¯at punch on a transversely isotropic piezoelectric half-space, we solve for their elastic and electric ®elds in smooth and frictional cases by ®rst evaluating the displacement functions and then di€erentiating. The displacement functions can be obtained by integrating the extended Boussinesq or Cerruti solutions in the contact region. Then, when only normal pressure is loaded, the stresses in the half-space of PZT-4 piezoelectric ceramic are compared in the ®gures with those of the transversely isotropic material which are assumed to have the same elastic constants as those of PZT-4. Meanwhile, the electric components in the half-space of PZT-4 piezoelectric ceramic are also shown in the same ®gures.