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Finite-element analysis of contact between elastic self-affine surfaces

“…Some approximate treatments of contact begin by assuming that the two surfaces do not deform and then determine the regions where the two solids would interpenetrate [2,3,6]. Scaling arguments [18] and simulations [18,30] show that this rigid overlap model gives a power law distribution of connected areas at large a c with τ = 2 − H/2.…”

“…However, recent experimental [2,3] and theoretical [6] papers have suggested a different view. They examine regions where undeformed surfaces would overlap and associate each with a contact.…”

“…Most surfaces are rough enough that atoms are only close enough to interact strongly in areas where peaks or asperities on opposing surfaces overlap. Experiments [1,2,3,4] and theory [5,6,7,8,9,10,11,12] show that this real area of contact A is often much smaller than the projected area A 0 of the surfaces. They have also correlated [1,2,3] the increase in friction with normal load W to a corresponding increase in A.…”

Frontiers of fundamental tribological research

“…However, any improvements in the ability to accurately measure contact properties should be matched by advances in modeling these systems. The fractal nature of many surfaces is likely to be crucial in correctly describing multi-asperity contacts and some progress has been made in this area [51][52][53][54][55][56]. These analyses are, however, only for a static contact and the problem of junction growth at the asperity contacts during sliding also needs to be addressed.…”

“…For static, well-defined, single-asperity contacts, significant insights have been achieved using the atomic force microscope [20,23]. For rough surfaces, recent advances have been made in understanding contact properties by building on earlier multi-asperity contact models [49][50][51][52][53][54] and by incorporating a fractal description of the surface [55][56][57][58][59]. Based on these approaches, complete solutions are envisioned in either the completely plastic or completely elastic limit.…”