Effects of surface tension and Steigmann–Ogden surface elasticity on Hertzian contact properties

Abstract

Surface tension, membrane stiffness and flexural rigidity all have been found to play significant roles in the determination of mechanical properties of nanosized materials and structures. In this work, Steigmann–Ogden theory of surface elasticity is applied for solving the contact properties between a rigid sphere and an elastic half-space. By integrating the surface Green’s function of the corresponding nonclassical Boussinesq solution, the mixed boundary-value problem is transformed into a pair of singular integral equations, which are subsequently reduced to a nonlinear algebraic system of equations by Gauss–Chebyshev quadrature. Extensive numerical studies are performed to investigate the coupling effects of surface tension, membrane stiffness and flexural rigidity on contact radius, contact pressure, contact stiffness and displacement and stress distributions in the half-space. For microsized rigid spherical indenters, the inclusion of Steigmann–Ogden surface theory results in appreciably smaller contact radius, lower contact pressure, displacements and stresses, thus leading to higher contact stiffness. This observation suggests the increasing importance of the half-space boundary in load-carrying capability as the strength of surface material properties increases or the indenter size decreases. Moreover, least-squares based regression analysis proves that, in the presence of surface effects, the distribution of contact pressure obeys an elliptical curve less than a half. In addition, the sharp corners that are conventionally found in classical contact stress and subsidence displacement are replaced by smooth transitions across the circular contact perimeter.