Contact responses of transversely isotropic layered material with imperfect interface

This paper establishes a contact model between a rigid sphere and transversely isotropic layered material with imperfect interface. Interfacial displacement and stress of the coating-substrate system are transmitted discontinuously because of coupled dislocation-like and force-like defects. General solution of elastic field for transversely isotropic material was derived first, which was further converted to frequency response functions (FRFs) by performing the Fourier transform. Considering coupled dislocation-like and force-like interfacial condition, closed-form analytical expressions of elastic field for transversely isotropic layered material with imperfect interface in the Fourier frequency domain were obtained, and the discrete convolution-fast Fourier transform (DC-FFT) algorithm was employed to calculate FRFs. A conjugate gradient method (CGM) was used to solve contact equations iteratively. The reduced model with perfect interface was validated by carrying out a corresponding example with the analytical solution method and the finite element method (FEM). Effects of uncoupled / coupled dislocation-like or/and force-like interface conditions on contact behaviors and stress distributions were investigated employing the proposed model.