Continuous contact problem of a system consisting of functionally graded orthotropic and isotropic layers bonded to a rigid foundation and under rigid punch loading

Functionally graded materials (FGMs) are a new generation of heterogeneous composite materials consisting of two or more phases with gradually varying microstructure and/or material composition. Due to the importance of these materials in engineering applications, their contact mechanics behaviour has been studied by numerous researchers. In this thesis, the continuous contact problem of a two-layer system consisting of FG orthotropic and FG isotropic layers is examined within the framework of elasticity theory. A static concentrated load is applied to the FG orthotropic layer via a rigid punch, while the FG isotropic layer is bonded to a rigid foundation at its lower surface. The formulation considers cases where the punch profile is either flat or cylindrical. The layers are placed on top of each other without being bonded, and all surfaces are assumed to be frictionless. To investigate the material orthotropy of the FG orthotropic layer, five different real orthotropic materials are used. The stiffness coefficients and density of the FG orthotropic layer, and the shear modulus and density of the FG isotropic layer vary exponentially along the heights of these layers. Using Fourier Cosine and Sine transforms, general expressions for stresses and displacements in both layers are obtained. The plane contact problem is reduced to a singular integral equation using the boundary conditions of the problem. Gauss-Chebyshev integration formulas are used to solve this integral equation numerically. As a result of the study, contact lengths, contact stress distributions, critical load factors and initial separation points are determined depending on various non-dimensionalized parameters and different orthotropic materials used.