Analysis of size-dependent response of surface excited functionally graded layer with consideration of couple-stress effects

Abstract

This paper focuses on a theoretical examination of the mechanical behavior of elastic layers made of functionally graded (FG) materials. It particularly highlights the impact of material microstructures by utilizing the couple stress theory to introduce FG characteristics of the coating material across the thickness direction, along with size effects. The study distinctively addresses both surface loading and contact problems, employing various indenter shapes and eccentric indentation forces. The Fourier transform is utilized to solve for displacements and stress fields resulting from surface tractions. The method for approximating the pressure distribution under the indenter is based on a collocation method with a simple discretization of the contact pressure. Brent's method is applied to determine the unknown contact region when using indenters with non-sharp edges. The results demonstrate that the shear modulus ratio and the intrinsic material length scale significantly influence the pressure intensity, highlighting a substantial dependence on the mechanical properties of materials under indentation force. The research also shows that the effect of the length scale and shear modulus ratio affects the limit eccentricity and tilt angle. The results highlight the necessity of considering both the size effect and material gradation when analyzing FG materials under mechanical stress.