A numerical model for the point contact of dissimilar materials considering tangential tractions

This paper presents a three-dimensional numerical model for the simulation of the contacts of elastically dissimilar materials. This model is based on the Boussinesq-Cerruti integral equations relating normal and tangential surface tractions to surface displacements and employs the static friction law to identify the onset of local micro-slip. An iterative conjugate gradient method (CGM) is utilized to determine the unknown contact and stick area efficiently and accurately with the assistance of the discrete convolution and fast Fourier transform (DC-FFT) algorithm. The model leads to the solutions of surface real contact and stick areas, pressure, tangential tractions, and the subsurface stress field. It is verified through the comparison of the numerical results with analytical solutions. Simulations are performed for a ball and half-space contact with the normal loading alone first, and then the results for the contact with increasing tangential loading are also presented. The effects of shear tractions on the contact area, the stick zone, pressure and the intensity of von-Mises stress are discussed.