A comprehensive parametric study of contact behavior in functionally graded bilayer systems

An extensive body of research in contact mechanics has been conducted due to its broad relevance to numerous engineering systems of practical interest. The investigation of contact behavior in deformable bodies represents a major challenge in engineering, as it plays a crucial role in the performance of structural and mechanical systems. Due to its importance, the field has received considerable attention in the literature. The present study focuses on analyzing the contact problem of a two-layered system composed of a functionally graded orthotropic layer (FGOL) and a functionally graded isotropic layer (FGIL). The layered system is fully bonded to a rigid substrate (RS), and frictional effects are neglected. No bonding is assumed between the two layers. The system is subjected to loading through a flat-ended rigid indenter (FERI), and the body forces of both layers are incorporated into the formulation. In the solution of the contact problem, the condition of constant vertical displacement (and thus its zero derivative) under the FERI is defined as the boundary condition; it is subsequently reduced to a singular integral equation through the application of Fourier integral transform techniques. This integral equation is subsequently solved numerically by applying the Gauss–Chebyshev integration formula. A comprehensive parametric study is conducted with respect to different material configurations and various dimensionless parameters, providing detailed insight into the mechanical response of the functionally graded layered system.