multi-asperity model; contact area.

Introduction
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Contact and friction interactions play an essential role in many quotidian contexts, including those related to industry and transportation (e.g., tire-road and wheel-rail contacts, electric switches, gears, bearings, and brake systems), everyday human activity (e.g., walking, handling, touching, and sitting) and natural phenomena (e.g., earthquakes, landslides, and glacier motion). Regardless of such prevalence, contact-related mechanisms (friction, adhesion, and wear) are still not fully understood and thus are among the most cutting-edge research topics in the mechanical community [@mo2009friction; @ben2010dynamics; @pastewka2011anisotropic; @aghababaei2016critical].

Numerous models of contact-related mechanisms exist at structural scale [@vakis2018]. They serve to model (1) interfacial normal and tangential stiffness [@wriggers1993application; @akarapu2011stiffness], (2) frictional resistance [@ruina1983slip], (3) material removal on rubbing surfaces (wear) [@archard1956wear; @yin2010adhesive], (4) heat transfer between contacting solids [@madhusudana1996thermal], (5) contact electric resistance [@slade2017electrical; @yastrebov2015holm], (6) adhesion [@fuller1975effect; @pastewka2014contact], (7) interfacial fluid flow [@dapp2012self; @dapp2016fluid; @shvarts2018trapped], (8) microstructural changes in near-contact material layers [@ramesh2008modeling], (9) fretting wear life-cycle [@hills1994mechanics; @fouvry1997wear; @dick2006fretting], (10) debris generation [@sayles1982influence; @basseville2011numerical], (11) lubrication [@patir1978average], and other mechanisms. The associated models can be incorporated in a macroscopic/structural model via constitutive interfacial equations. These equations can be based either on experimental data, and thus remain purely phenomenological, 