Analytical approaches to describe wear in total knee replacements: potentials and limitations

Various types of wear mechanisms (three-body wear, delamination, pitting, abrasion, etc.) can occur between the polymer-metal interface of total knee arthroplasties. In most cases, the mechanism of these types of wear has only been experimentally verified and described. It must be noted that analytical description is not yet available for the majority of wear types. An exception among these types is abrasive wear, for which a number of analytical studies have been developed. This kind of wear can be approximated mathematically by the so-called Archard equation. It should be noted that, due to the complex motion of the knee joint, the original Archard equation must be extended by several parameters in order to adequately describe the wear process. Such parameters are the cross shear ratio, the coefficient of friction or the slide-roll ratio. The present study gives a broad overview of the currently available analytical wear models and also provides further suggestions on how to bring these models closer to reality.