Approaches to solving viscoelastic problems have received extensive attention in recent decades as viscoelastic materials have been widely applied in various fields. An overview of relevant modelling approaches is provided in the paper. The review starts with a brief introduction of some basic terminologies and theories that are commonly used to describe the contact behaviour of viscoelastic materials. By building up the complexity of contact problems, including dry contact, lubricated contact, thermoviscoelastic contact and non-linear viscoelastic contact, tentative analytical solutions are first introduced as essential milestones. Afterwards, a series of numerical models for the various types of contact problems with and without surface roughness are presented and discussed. Examples, in which computational tools were employed to assist the analysis of viscoelastic components in different fields, are given as case studies to demonstrate that a comprehensive numerical framework is currently being developed to address complex viscoelastic contact problems that are prevalent in real life.

Tribochemistry plays a very important role in the behaviour of systems in tribologically loaded contacts under boundary lubrication conditions. Previous works have mainly reported contact mechanics simulations for capturing the boundary lubrication regime, but the real mechanism in which tribofilms reduce wear is still unclear. In this paper, the wear prediction capabilities of a recently published mechanochemical simulation approach (Ghanbarzadeh et al. in Tribol Int, 2014) are tested. The wear model, which involves a time- and spatially dependent coefficient of wear, was tested for two additive concentrations and three temperatures at different times, and the predictions are validated against experimental results. The experiments were conducted using a mini-traction machine in a sliding/rolling condition, and the spacer layer interferometry method was used to measure the tribofilm thickness. Wear measurements have been taken using a white-light interferometry. Good agreement is seen between simulation and experiment in terms of tribofilm thickness and wear depth predictions.