Closed-form solution of the two-dimensional sliding frictional contact problem for an orthotropic medium

•Singular integral equation approach is used.•Closed-form solutions for the contact stresses are obtained.•Krenk terminology is used for orthotropic material parameters.•Shear parameter, κκ, has a significant effect on the contact stresses.•The influence of the stiffness ratio parameter, δδ, on the powers of stress singularity is not significant.

The two-dimensional frictional contact problem of a rigid stamp sliding over an orthotropic medium is considered. The coordinate system is chosen such that it is aligned with the principal axes of orthotropy. It is parallel and perpendicular to the contact surface which is located along the x1x1 axis. It is assumed that the condition of Coulomb friction prevails on the contact area. The two-dimensional half-plane problem is formulated using the Fourier integral transform method and the analytical formulation of the contact problem is reduced to a Cauchy-type singular integral equation of the second kind for the unknown contact pressure. The singular integral equation is solved analytically utilizing the Jacobi polynomials. With the application of the results to the crack initiation in an orthotropic medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state at either end of the flat stamp and on the determination of the contact stresses based on orthotropic material parameters. The present study provides the analytical solution of the contact stresses in terms of orthotropic material parameters, the coefficient of friction and the spatial coordinates. The strength of the singularities and the stress intensity factors at both ends of the stamp are also found in terms of the orthotropic material parameters and the coefficient of friction. This study reveals that orthotropic material parameters and the coefficient of friction have a great effect on the strength of stress singularities and distribution of the contact stresses. Adjusting these parameters will reduce these stresses that may have a bearing on the failure of the orthotropic medium. The results of this study will provide benchmark results for finite element analysts and stress engineers.