Analysis of two-dimensional rigid cylindrical indentation problems based on consistent couple stress elasticity

Abstract

In this paper, within the framework of the consistent couple stress elasticity theory, Green's functions are derived for the half-plane using Mindlin’s potential function method and Fourier transform technology. Using the general solution for a micro-structured elastic half-plane under concentrated load, we investigate the two-dimensional indentation problem beneath a rigid cylindrical indenter. Due to the complexity of the integral kernel, deriving an analytical solution is difficult. Therefore, we decompose it into a singular part and a regular part and numerically solve it using the Gauss–Chebyshev quadrature formula. Furthermore, we present a generalized expression for the pressure distribution incorporating scale effects and establish functional relationships among the contact half-width, applied load, and scale parameter, and compared with the numerical results. The results indicate that the elastic displacement response under the consistent couple-stress theory differs significantly from that in classical elasticity. The asymptotic behavior of the displacement components is influenced by the material length scale parameter, and the rotation becomes bounded. These findings contribute to the understanding of mechanical characteristics in micro-indentation tests and can be applied to simulate macroscopic responses in polymers or other composite materials affected by microscale influences.