Prandtl-Tomlinson Model: A Simple Model Which Made History

Abstract

One of the most popular models widely used in nanotribology as the basis for many investigations of frictional mechanisms on the atomic scale is the so-called Tomlinson model, consisting of a point mass driven over a periodic potential. The name “Tomlinson model” is, however, historically incorrect: The paper by Tomlinson from the year 1929 which is often cited in this context did not, in fact, contain the model known as the “Tomlinson model” and suggests, instead, an adhesive contribution to friction. In reality, it was Ludwig Prandtl who suggested this model in 1928 to describe the plastic deformation in crystals and dry friction. Staying in line with some other researchers, we call this model the “Prandtl-Tomlinson model,” although the model could simply and rightly be dubbed the “Prandtl model.” The original paper by Ludwig Prandtl was written in German and was not accessible for a long time for the largest part of the international tribological community. The present paper is a historical introduction to the English translation of the classical paper by Ludwig Prandtl, which was published in 2012. It gives a short review of the model as well as its properties, applications, and extensions from a contemporary point of view.