Despite considerable effort, multiscale models in tribology, pioneered probaby by Archard in the 1950's well before the world "fractal" was popularized by Benoit Mandelbrot, have managed to obtain only limited success, and mostly qualitative rather than quantitative. As proved by Ciavarella et al. in 1999, the "real" contact area in elastic contact of fractal surfaces is a fractal itself, and this was confirmed later by Persson's model, and by many numerical studies. This implies the need to "truncate" many descriptions of tribological phenomena (friction, adhesion, wear, etc.) at some "cutoff" scale, which becomes often crucial in determining some quantities. Some exceptions occur in adhesion, where the BAM (Bearing Area Model) of Ciavarella has proved that the cutoff short scale truncation is not important to determine stickiness of real fractal surfaces. We describe some of the development of these multiscale models in tribology of the last 20 years, with particular emphasis on the case of adhesion, but with some reference also to friction models, wear models, and the recent work on the coupling of geometrical effects with viscoelasticity, which tends to give a larger enhancement of adhesion than small roughness, making it possible in principle to obtain novel attachment devices for robotic applications and energy saving techniques in gripping and transportation of components in manufacturing.
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