On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods

The frictionless double receding contact problem for two functionally graded (FG) layers pressed by a uniformly distributed load is addressed in this paper. The gradation in the layers is assumed to follow an exponential variation through the height with constant Poisson's ratios. The lower layer rests on a homogeneous half-plane (HP). There is no adhesion between the FG layers or between the lower layer and the HP. The body forces of the FG layers and HP are ignored. First, the governing equations are reduced to a system of two singular integral equations with contact pressures and contact lengths as unknowns using Fourier transform techniques and boundary conditions. The integral equations are solved numerically using the Gauss-Chebyshev integration formula. Then, a parametric finite element analysis is performed using the augmented contact method. Finally, the problem was extended based on the multilayer perceptron (MLP), an artificial neural network used for different problem parameters. The effects of stiffness parameters, the normalized load length, the ratio of shear moduli, the ratio of FG layer heights to the normalized contact lengths, and normalized maximum contact pressures are explored. The results of finite element analysis and the MLP approach are used to validate the normalized maximum contact pressures and contact lengths obtained from an analytical method based on elasticity theory, and finally, good agreement between these three methods results is obtained. The obtained results could help in designing multibody indentation systems with FGMs.