Theory of moving contact of anisotropic piezoelectric materials via real fundamental solutions approach

A general theory for the moving contact behaviors of anisotropic piezoelectric materials under the action of a rigid flat or cylindrical punch is proposed. It is assumed that the punch is either a perfectly electric conductor or a perfectly electric insulator. The Galilean transformation, Fourier sine and cosine transforms are employed to solve the piezoelectric governing equations containing the inertial terms. The characteristic equation is a double-biquadrate equation. A detailed analysis is performed for the eigenvalue distribution and real fundamental solutions are derived for each eigenvalue distribution. The originally mixed boundary value problem is reduced to the Cauchy integral equations and then exact solutions to these integral equations are obtained for the conducting or insulated punch with the flat or cylindrical punch profile. Finally, closed-form expressions for the stresses and electric displacements are derived. The present analysis provides a scientific basis for the interpretation of contact behaviors of anisotropic piezoelectric materials.