The contact of rough surfaces has been studied for a long time, with the hope to explain fiction, adhesion. wear and
other tribological problems, This has given rise to a numberof “academic problems", since roughness itself has generated a number of
multiscale and factal models which seem mathematically required to
describe the geometry. Some considerable progress has been
made in the area of elastic contact. where we know in details the solution for nominally flat,
infinite surfaces (Persson's solution).
However, friction has been studied since the times of Leonardo and in 500 years, no predictive model has emerged. mainly qualitative understanding only has emerged from rough contact models, For adhesion. we are making progress and we describe here a recent model
BAM by Ciavarella. Recenly, rough contact models have also been attempted in the hope to predict the coellicient of proportionality behween wear loss and fiction dissipation which was observed already bv Reve in 1860, and then Archard in the 1950's. A recent theory by Persson shows some hopes to make progress, but opens also some problems.
