Contact analysis for anisotropic elastic materials considering surface stress and surface elasticity

Abstract

Contact analysis for an anisotropic elastic half-space is performed using the surface Green's function considering surface stress and surface elasticity. The discrete convolution and fast Fourier transform (DC–FFT) method and the conjugate gradient (CG) method was used to conduct the contact analysis. The influence coefficient in the contact analysis is calculated using the surface Green's function. The depth used employed in the surface Green's function considering surface stress and surface elasticity was decided such that the results of contact analysis of a rigid spherical indenter using Green's function for several values of depth agreed with the results of MD analysis. Several contact analyses were conducted in order to investigate the effects of material anisotropy and surface properties on the penetration depth for the ridge orientation in elliptic, Knoop, Vickers, and Berkovich indenters. When used to penetrate the (100) and (111) surfaces of Cu or Al, the penetration depth on indenter orientation clearly indicates material anisotropy in the elliptic and Knoop indenters, and indicates only a slight effect of material anisotropy in the Vickers and Berkovich indenters. The displacement field considering surface stress and surface elasticity is rounded in comparison with the shape of each crystal structure.