On the frictional receding contact between a graded layer and an orthotropic substrate indented by a rigid flat-ended stamp

Abstract This paper solves the frictional receding contact between a functionally graded elastic layer and an orthotropic substrate under the indentation of a rigid flat-ended stamp. Both normal and tangential indentation forces, satisfying Coulomb's friction law, are considered. The shear modulus of the graded layer is assumed to vary exponentially along the transverse dimension, whereas the Poisson's ratio is fixed as a constant. Under the plane strain sliding condition, the governing equations and boundary conditions of the double contact problem are converted into dual singular integral equations with the help of Fourier integral transforms. Gauss-Jacobi quadratures of different kinds and an iterative algorithm are subsequently developed to determine the stationary contact pressure, the receding contact pressure as well as the asymmetric receding contact boundaries. In order to verify and validate the accuracy of semianalytical solutions, the graded finite element modelings are also implemented through defining material properties of the graded layer at the Gaussian integral points of all elements and communicating with the major solver in terms of a user-defined interface. Parametric studies primarily focus on the effects of frictional coefficients, stiffness orthotropy and gradation on the stationary and receding contact properties. The influence of indenter size and thickness ratio between the graded layer and the orthotropic substrate is also investigated. Reasonable agreements of contact pressures and receding contact lengths are identified between the solutions obtained from two independent approaches. Extensive parametric studies provide an effective means of tailoring the double contact properties as desired by the appropriate selection of governing parameters.