A numerical method based on Polonsky-Keer's conjugate gradient iterative scheme for solving axisymmetric contact of layered half-space

Abstract

Axisymmetric contact analysis of layered half-space is of considerable interest in many tribological applications including protective hard coating, metal-matrix composites, etc. Polonsky-Keer's iterative scheme based on conjugate gradient method (CGM) is powerful for a general three-dimensional contact problem using rectangular meshes, but would inevitably lead to excessive computational burden and inaccurate boundary discretization for axisymmetric contact. In this paper, Polonsky-Keer's CG-based iterative scheme is adapted for axisymmetric indentation of a layered elastic half-space by taking advantage of annular ring discretization, where the elementary solutions for the surface deflection and subsurface stresses can be determined with assistance of the Hankel transforms. The present method can not only effectively circumvent the discretization error, but is also versatile and flexible to solve the contact between the layered materials and an arbitrary axisymmetric indenter. Parametric studies are provided to validate the present solutions, and the comparisons of the average relative errors for different types of elements are conducted to demonstrate the excellent convergence and accuracy of the proposed numerical scheme.