Computational contact mechanics for a medium consisting of\rfunctionally graded material coating and orthotropic substrate

This paper presents a semi-analytical method to investigate the frictionless contact mechanics between a\rfunctionally graded material (FGM) coating and an orthotropic substrate when the system is indented by a\rrigid flat punch. From the bottom, the orthotropic substrate is completely bonded to the rigid foundation. The\rbody force of the orthotropic substrate is ignored in the solution, while the body force of the FGM coating is\rconsidered. An exponential function is used to define the smooth variation of the shear modulus and density\rof the FGM coating, and the variation of Poisson’s ratio is assumed to be negligible. The partial differential\requation system for the FGM coating and the orthotropic substrate is solved analytically through Fourier\rtransformations. After applying boundary and interface continuity conditions to the mixed boundary value\rproblem, the contact problem is reduced to a singular integral equation. The Gauss–Chebyshev integration\rmethod is then used to convert the singular integral equation into a system of linear equations, which are\rsolved using an appropriate iterative algorithm to calculate the contact stress under the rigid flat punch. The\rparametric analyses presented here demonstrate the effects of normalized punch length, material\rinhomogeneity, dimensionless press force, and orthotropic material type on contact stresses at interfaces,\rcritical load factor, and initial separation distance between FGM coating and orthotropic substrate. The\rdeveloped solution procedures are verified through the comparisons made to the results available in the\rliterature. The solution methodology and numerical results presented in this paper can provide some useful\rguidelines for improving the design of multibody indentation systems using FGMs and anisotropic materials.