Solutions of the generalized half-plane and half-space Cerruti problems with surface effects

Abstract

The generalized half-plane and half-space Cerruti problems with surface effects are analytically solved using Gurtin and Murdoch’s surface elasticity theory along with the Airy stress function method and the Papkovitch–Neuber potential function approach, respectively. The Fourier transform method is employed in the formulation. The newly derived solutions reduce to their classical elasticity-based counterparts if the surface effects are not considered. In addition, the current solution for the half-space Cerruti problem recovers that based on a simplified version of the surface elasticity theory as a special case. Further, specific solutions are obtained for the cases with loading by a concentrated tangential force and by a uniform traction acting over a circular region. The numerical results reveal that the predictions by the current solutions substantially deviate from those by their classical counterparts near the loading site, but the differences between the two sets of predictions diminish far away from the loading site. Moreover, the newly obtained solutions do not exhibit stress or displacement singularity at the loading point/boundary and predict smoother stress fields and smaller displacements than the classical solutions that do not incorporate the surface effects.