Frictional contact problem of a coated half plane pressed by a rigid punch with coupled stress elasticity

This paper considers the size-dependent plane frictional contact problem of a homogeneous coated half-plane indented by a rigid punch based on the couple stress elasticity. Using the Fourier integral transform technique in addition to the boundary and compatibility conditions, the mixed-boundary value problem is converted into a singular integral equation of the second kind. The integral equation is further derived and normalized for the cylindrical and flat punch case profiles. Applying the Gauss–Jacobi integration formula, the resulting singular integral equation is reduced to a system of algebraic equations. The obtained results are first validated based on those published for the case of a frictionless contact problem of a half-plane indented by rigid cylindrical and flat punches and solved based on the couple stress theory. A detailed parametric study is then performed to investigate the effect of the characteristic material length, the friction coefficient, the layer height, the shear modulus, the indentation load and Poisson’s ratio on the contact and in-plane stresses.