Sliding frictional contact analysis of an elastic solid with couple stresses

Abstract This paper investigates the two-dimensional sliding frictional contact of an elastic solid in the plane strain state based on the theory of the couple stress elasticity. This theory introduces the characteristic material length in order to describe the size effect caused by the underlying microstructure. The Coulomb type friction is assumed in the analysis. The size-dependent contact problem of the rigid flat, cylindrical and parabolic punches is formulated in terms of the Cauchy singular integral equation of the second kind. Then, it is solved numerically to determine the distribution of the normal contact stress and in-plane stress at the contact surface. The effects of the small scale parameter and the friction coefficient on the surface normal and in-plane stresses are discussed in detail. It is found that the contact stress predicted by the couple stress elasticity shows a significant departure from that predicted by the classical elasticity for the half-plane subjected to the same punch and load.