Modelling tangential contact problem with surface stress

In this paper, we investigate the effects of surface stress on the spherical contact problem under combined normal and lateral loads. The boundary element method based on fast Fourier transform and conjugate gradient algorithm is employed to perform the contact analysis with partial slip. It is shown that as the size of contact reduces to the characteristic scale that surface stress dominates, the contact behavior will significantly deviate from the classical model. Under the same loading condition, the tangential traction within contact region tends to distribute more evenly and the width of slip zone would be relatively smaller due to the presence of surface stress. In addition, it is found that the variations of the total tangential force and the lateral contact stiffness with respect to the lateral displacement depend strongly on the contact scale. This work provides a theoretical basis for the study of contact and friction of some soft materials and biological systems.