A SAM-FFT based model for 3D steady-state elastodynamic frictional contacts

Abstract

This paper reported a semi-analytical method (SAM)-fast Fourier transform (FFT) based model for three-dimensional (3D) steady-state elastodynamic frictional contact of an elastic ellipsoid sliding on an elastic half-space with a constant sliding velocity. The frequency response functions (FRFs) and their conversion into influence coefficients (ICs) for displacements and stresses in an elastic half-space are analytically derived pertaining to generalized normal and tangential forces. Fast numerical techniques used are based on the conjugate gradient method (CGM) for obtaining unknown pressure distribution in the contact interface, and the discrete convolution-fast Fourier transform (DC-FFT) algorithm for calculating displacements and stresses. The proposed SAM-FFT based model is employed to investigate the effects of friction, sliding velocity, and Young's modulus on contact pressure, surface deformation and sub-surface von Mises stress. A transition map, supported by appropriate limits of friction coefficient and sliding velocity, is constructed to determine whether the location of maximum von Mises stress to appear beneath the contact surface or in the contact surface. It deserves mentioning that the elastodynamic effect becomes more profound if the sliding velocity is higher than 0.4 times of shear wave speed, which corresponds to a sliding velocity of 1300 m/s for steel materials (shear wave speed ∼3250 m/s), or 60 m/s for a soil foundation (shear wave speed ∼150 m/s).