The full understanding of the viscoelastic contact mechanics between rough surfaces is a crucial issue in modern engineering research. This paper investigates the role that the number of rough scales, i.e. the cut-off of the power spectrum of the surface roughness, has on quantities like contact area, mean separation, and friction. Furthermore, an effective, though approximate, definition of an equivalent modulus is provided in order to reduce the viscoelastic contact domain to an elastic equivalent one.
GreenwoodJAWilliamsonJBP. Contact of nominally flat surfaces. Proc R Soc Lond A1966; 295: 300–319.
2.
GreenwoodJA. A simplified elliptic model of rough surface contact. Wear2006; 261: 191–200.
3.
GreenwoodJAPutignanoCCiavarellaM. A Greenwood & Williamson theory for line contact. Wear2011; 270: 332–334.
4.
BushAWGibsonRDThomasTR. The elastic contact of a rough surface. Wear1975; 35: 87–111.
5.
CiavarellaMDelfineVDemelioG. A “re-vitalized” Greenwood and Williamson model of elastic contact between fractal surfaces. J Mech Phys Solids2006; 54: 2569–2591.
6.
PerssonBNJ. Theory of rubber friction and contact mechanics. J Chem Phys2001; 115: 3840–3861.
CiavarellaMGreenwoodJAPaggiM. Inclusion of “interaction” in the Greenwood and Williamson contact theory. Wear2008; 265: 729–734.
9.
PaggiMCiavarellaM. The coefficient of proportionality between real contact area and load, with new asperity models. Wear2010; 268: 1020–1029.
10.
PutignanoCAfferranteLCarboneG. A new efficient numerical method for contact mechanics of rough surfaces. Int J Solid Struct2012; 49: 338–343. DOI: 10.1016/j.ijsolstr.2011.10.009.
11.
CarboneGScaraggiMTartaglinoU. Adhesive contact of rough surfaces: comparison between numerical calculations and analytical theories. Eur Phys J E Soft Matter2009; 30: 65–74.
12.
GeikeTPopovVL. Mapping of three-dimensional contact problems into one dimension. Phys Rev E2007; 76: 036710–036710.
13.
ScaraggiMPutignanoCCarboneG. Elastic contact of rough surfaces: a simple criterion to make 2D isotropic roughness equivalent to 1D one. Wear2013; 297: 811–817.
14.
HyunSPeiLMolinariJ-F. Finite-element analysis of contact between elastic self-affine surfaces. Phys Rev E2004; 70: 026117–026117.
15.
YangCTartaglinoUPerssonBNJ. A multiscale molecular dynamics approach to contact mechanics. Eur Phys J E Soft-Matter2006; 19: 47–58.
16.
YangCPerssonBNJ. Molecular dynamics study of contact mechanics: contact area and interfacial separation from small to full contact. Phys Rev Lett2008; 100: 024303–024303.
17.
CampanaCMuserMH. Contact mechanics of real vs. randomly rough surfaces: a Green’s function molecular dynamics study. Europhys Lett2007; 77: 38005–38005.
18.
GroschKA. The relation between the friction and visco-elastic properties of rubber. Proc R Soc Lond A Math Phys1963; 274: 21–39.
19.
PutignanoCReddyhoffTCarboneG. Experimental investigation of viscoelastic rolling contacts: a comparison with theory. Tribol Lett2013; 51: 105–113.
20.
CarboneGPutignanoC. Rough viscoelastic sliding contact: theory and experiments. Phys Rev E2014; 89: 032408–032408.
21.
FelhõsDXuDSchlarbAK. Viscoelastic characterization of an EPDM rubber and finite element simulation of its dry rolling friction. eXPRESS Polym Lett2008; 23: 157–164.
22.
HarrassMFriedrichKAlmajidAA. Tribological behavior of selected engineering polymers under rolling contact. Tribol Int2010; 43: 635–646.
23.
PutignanoCAfferranteLCarboneG. The influence of the statistical properties of self-affine surfaces in elastic contact: a numerical investigation. J Mech Phys Solids2012; 60: 973–982.
24.
DappWBProdanovNMüserMH. Systematic analysis of Persson’s contact mechanics theory of randomly rough elastic surfaces. J Phys Condens Matter2014; 26: 355002–355002.
25.
HyunSRobbinsMO. Elastic contact between rough surfaces: effect of roughness at large and small wavelengths. Tribol Int2007; 40: 1413–1422.
PutignanoCAfferranteLCarboneG. A multiscale analysis of elastic contacts and percolation threshold for numerically generated and real rough surfaces. Tribol Int2013; 64: 148–154.
28.
ScaraggiMPerssonBNJ. Friction and universal contact area law for randomly rough viscoelastic contacts. J Phys Condens Matter2015; 27: 105102–105102.
29.
PutignanoCCarboneGDiniD. Mechanics of rough contacts in elastic and viscoelastic thin layers. Int J Solid Struct2015; 69–70: 507–517. DOI: 10.1016/j.ijsolstr.2015.04.034.
30.
Christensen RM. Theory of viscoelasticity. New York: Academic Press.
31.
CarboneGPutignanoC. A novel methodology to predict sliding/rolling friction in viscoelastic materials: theory and experiments. J Mech Phys Solid2013; 61: 1822–1834. DOI: 10.1016/j.jmps.2013.03.005.
