Three-dimensional contact analysis with couple stress elasticity

Abstract This study establishes a size-dependent three-dimensional semi-analytical model (SAM) on the contact of an elastic half-space indented by a rigid sphere within the framework of couple stress elasticity. A characteristic material length is used to describe the size-dependent contact behaviors. The frequency response functions (FRFs) of the displacements and stresses are analytically derived with incorporating the effects of the characteristic material length, which are then converted to the corresponding influence coefficients (ICs). By using the conjugate gradient method (CGM), the surface pressure distribution is obtained, and the stress field beneath the contact surface is calculated with the fast Fourier transform (FFT). The proposed model is implemented to analyze the combined effects of the characteristic material length and Poisson's ratio on the size-dependent contact behaviors. A transition value of the characteristic material length is found, above which the size-dependent contact modeling is required, and below which the size-dependent behaviors can be ignored. Finally, the present model deals with some typical contacts involving different indenter shapes and multi-indenters, which is difficult to be implemented in the case of two-dimensional contact.