Some observations on Persson's diffusion theory of elastic contact

Persson's work on contact between tyres and roads led him to develop a theory of elastic contact which is of potentially much wider application. It involves the derivation of a diffusion equation, which is then solved, with the requirement that there should be no tension at the contact interface being imposed on the solution by means of a boundary condition. In this paper, the authors critically examine this approach and its results. It is found that Persson's proof is not rigorous and that the solutions, whilst being qualitatively reasonable and in accordance with other available solutions, differ from them quantitatively, predicting contact areas that are somewhat smaller and hence pressures that are larger than others have found. Given that these other solutions are also based on assumptions and approximations, a definitive solution of the elastic contact problem remains elusive.