Continuous and discontinuous contact problem of a functionally graded orthotropic layer indented by a rigid cylindrical punch: Analytical and finite element approaches

Abstract

In this study, the continuous and discontinuous contact problems of a functionally graded (FG) orthotropic layer lying on a homogeneous and isotropic layer were investigated. The orthotropic layer was indented by a rigid cylindrical punch which was subjected to a concentrated normal force, and a homogeneous isotropic layer was firmly attached to a rigid substrate. For the analytical solution, the general expressions for the stresses and displacements were obtained in the presence of body forces by using elasticity theory and Fourier integral transforms. The continuous and discontinuous contact problems were reduced to the singular integral equations by means of boundary conditions. The system of the singular integral equations was solved using the Gauss-Chebyshev integration formula. Then, the finite element solution of the two cases was also performed. Analytical results and numerical results (FEM) for critical load, initial separation distance, separation region in discontinuous contact, contact lengths under the punch, and contact stress distributions between the layer-punch and layer-layer were obtained for the dimensionless quantities.