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The design of machine elements made by viscoelastic matrix can be improved by numerical analysis. The solution of the viscoelastic contact problem with prescribed geometry is difficult to obtain because (1) both contact area and pressure distribution are a priori unknown, and (2) the contact parameters keep changing with time, together with the compliance of the viscoelastic material. These difficulties are overcome in this paper by conducting numerical analysis based on both spatial and temporal model discretization. The viscoelastic contact process simulation is achieved by computing a series of subsequent contact states, the current state depending on the entire contact history. In this manner, the memory effect of the viscoelastic material is accounted for. The numerical predictions agree well with the classic solution of the spherical contact undergoing step loading. The history of pressure distribution and modification of contact area in the finite length line contact between a rigid profiled roller and a polymethyl methacrylate viscoelastic half-space are obtained. The case when the normal force is applied eccentrically in the longitudinal direction, leading to a tilting moment, is also considered. © 2018 Published by Faculty of Engineering Corresponding author: S. Spinu Department of Mechanics and Technologies, Stefan cel Mare University of Suceava, 13th University Street, 720229, Suceava, Romania. E-mail: sergiu.spinu@fim.usv.ro

Viscoelastic Contact Modelling: Application to the Finite Length Line Contact