Surface effect on the contact problem of a piezoelectric half-plane

Based on the theory of the surface piezoelectricity, the two-dimensional frictionless contact problem of the piezoelectric half-plane under rigid flat and cylindrical punches is investigated in this paper. The Fourier integral transform method is adopted to derive the fundamental solution for the contact problem of piezoelectric materials with the surface effect, including the residual surface stress, surface elastic constant, surface piezoelectric constant and surface dielectric constant. Then, the contact problem is solved numerically to determine the distribution of the normal contact stress, in-plane stress and electric displacement at the contact surface. The surface effect on the normal contact stress, in-plane stresses and in-plane electric displacement is discussed in detail. We find that the surface effect plays a significant role on contact behaviors of piezoelectric materials at micro/nano-scales