Archard equation

The Archard wear equation is a simple model used to describe sliding wear and is based on the theory of asperity contact. The Archard equation was developed later than the Reye's hypothesis, though both came to the same physical conclusions, that the volume of the removed debris due to wear is proportional to the work done by friction forces. Reye’s model became very popular in Europe and it is still taught in university courses of applied mechanics. This theory has, however, been totally ignored in English and American literature where subsequent works by Ragnar Holm and John F. Archard are usually cited.

where:

Note that ${\displaystyle WL}$ is proportional to the work done by the friction forces as described by Reye's hypothesis.

The equation can be derived by first examining the behavior of a single asperity.

The local load ${\displaystyle \,\delta W}$, supported by an asperity, assumed to have a circular cross-section with a radius ${\displaystyle \,a}$, is:

...
Wikipedia