Rolling contact on a viscoelastic multi-layered half-space

Abstract

This paper’s purpose is the contact of a rolling body on a viscoelastic multi-layered half-space. Firstly, the contact is formulated with the classical definition of the gap and the pressure states in the contact zone and outside. L layers are considered on a substrate, L being any positive integer. Secondly, the influence coefficients related to an elastic multi-layered half-space are found, using the Papkovich–Neuber potentials. Tractions and displacements continuity is assumed at the interfaces, and then a construction of matrix systems corresponding to a unit pressure and a unit shear imposed at the top surface, leads to the general problem to solve. Further, the solution for any kind of pressure and/or shear distributions at the contact surface is inferred by convolution with the influence coefficients found earlier, using the Fast Fourier Transform (FFT) algorithms. Throughout the steps, an Elastic/Viscoelastic correspondence is used in order to take into account not only the change of behaviour of the half-space during time, but also to superpose the load history. Conjugate Gradient Method (CGM) algorithms are used to solve the variational problem that yields from the contact problem definition. In the present paper, a parametric study is performed to highlight the effects of the elastic modulus and the relaxation time on some relatively simple cases of rolling contact.