On the nanoindentation of a couple-stress half-plane with Steigmann–Ogden surface effects

This article presents a comprehensive investigation into the nanocontact mechanics of an elastic half-plane indented by a rigid circular indenter, accounting for both surface and couple-stress effects. To capture the surface phenomena at the upper boundary of the half-plane, the Steigmann–Ogden surface elasticity model is employed, while the bulk material is described using the classical asymmetric couple-stress theory. We derive the nonclassical boundary conditions and, combined with the continuity of displacements at the contact interface, formulate the integral equation governing the nanocontact problem through the application of Fourier integral transforms. The Gauss–Chebyshev numerical quadrature method is then applied to discretize and collocate the integral equation, supplemented by the force equilibrium condition. The accuracy and robustness of the proposed solution method are validated through comparison with existing literature results. A series of parametric studies are conducted to elucidate the critical influence of both surface and couple-stress effects on the size-dependent elastic behavior of the half-plane. When the contact area is equivalent to the order of magnitude of the characteristic material lengths associated with the bulk and surface, we explore the relative contributions of these two effects at the nanoscale, including the distinctive impact of surface flexural rigidity inherent to the Steigmann–Ogden model. The findings highlight the necessity of incorporating both surface and couple-stress effects in the design and analysis of nanostructured materials, particularly when the scale of the contact region approaches nanometer dimensions.