Abstract
This chapter reviews recent advances made in the treatment of contact problems involving soft materials often characterized by non-linearly elastic material properties, such as rubber and soft biological tissues. Starting from the fundamental formulation developed to solve viscoelastic contact mechanics, the treatment of complex problems involving surface roughness, layered materials, and reciprocating contacts in dry contacts is presented in increased order of complexity. The reader is then introduced to the study of lubricated contacts, with a discussion of the interplay between viscoelastic effects in the solids and the viscosity marking the lubricant behavior. Experimental validations that cover various aspects of the work are also presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Here, scatter is defined as \(\sigma /\mu \), i.e., the ratio between the standard deviation \(\sigma \) and the mean measured value \(\mu \).
References
Akarapu, S., Sharp, T., & Robbins, M. O. (2011). Stiffness of contacts between rough surfaces. Physical Review Letters, 106, 204301.
Almqvist, A., Campañá, C., Prodanovb, N., & Persson, B. N. J. (2011). Interfacial separation between elastic solids with randomly rough surfaces: Comparison between theory and numerical techniques. Journal of the Mechanics and Physics of Solids, 59, 11.
André, T., Lévesque, V., Hayward, V., Lefèvre, P., & Thonnard, J.-L. (2011). Effect of skin hydration on the dynamics of fingertip gripping contact. Journal of the Royal Society Interface, 8, 64.
Archard, J. F., & Hirst, W. (1956). Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 236, 397.
Barber, J. R. (2003a). Bounds on the electrical resistance between contacting elastic rough bodies. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 459, 53–66.
Barber, J. R. (2003b). Bounds on the electrical resistance between contacting elastic rough bodies. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 459, 53–66.
Barber, J. R. (1974). Determining the contact area in elastic indentation problems. Journal of Strain Analysis, 9, 230–232.
Barber, J. R., Davies, M., & Hills, D. A. (2011). Frictional elastic contact with periodic loading. International Journal Solids Structures, 48, 2041–4047.
Barenblatt, G. I. (1996). Scaling, self-similarity and intermediate asymptotics. Cambridge: Cambridge University Press.
Bazrafshan, M., de Rooij, M., Valefi, M., & Schipper, D. (2017). Numerical method for the adhesive normal contact analysis based on a Dugdale approximation. Tribology International, 112, 117–128.
Bhushan, B. (2004). Springer handbook of nanotechnology. Berlin, Heidelberg, New York: Springer.
Bjorkland, S. (1997). A random model for micro-slip between nominally flat surfaces. ASME Journal of Tribology, 119, 726–732.
Borri Brunetto, M., Chiaia, B., & Ciavarella, M. (2001). Incipient sliding of rough surfaces in contact: A multi-scale numerical analysis. Computer Methods in Applied Mechanics and Engineering, 190, 6053–6073.
Bottiglione, F., Carbone, G., & Mantriota, G. (2009a). Fluid leakage in seals: An approach based on percolation theory. Tribology International, 42(5), 731–737.
Bottiglione, F., Carbone, G., Mangialardi, L., & Mantriota, G. (2009b). Leakage mechanism in flat seals. Journal of Applied Physics, 106, 104902.
Bowden, F. P., & Tabor, D. (2001). The friction and lubrication of solids. Clarendon Press.
Bowden, F. P., & Tabor, D. (1939). The friction and lubrication of solids. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 169, 391.
Bruggeman, D. A. G. (1935). Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. Ann. Phys. (Leipzig), 24, 636–679.
Bureau, L., Caroli, C., & Baumberger, T. (2003). Elasticity and on set of frictional dissipation at a non-sliding multi-contact interface. Proceedings Royal Society (London). A, 459, 2787–2805.
Bush, A. W., Gibson, R. D., & Thomas, T. R. (1975). The elastic contact of a rough surface. Wear, 35, 87–111.
Campana, C., Mueser, M. H., & Robbins, M. O. (2008). Elastic contact between self-affine surfaces: Comparison of numerical stress and contact correlation functions with analytic predictions. Journal of Physics-Condensed Matter, 20(35), 354013.
Campana, C., & Muser, M. H. (2007). Contact mechanics of real vs. randomly rough surfaces: A Green’s function moleculardynamics study. Europhysics Letters, 77(3), 38005.
Campana, C., Persson, B. N. J., & Muser, M. H. (2011). Transverse and normal interfacial stiffness of solids with randomly rough surfaces. Journal of Physics-Condensed Matter, 23(8), 085001.
Carbone, G., & Persson, B. N. J. (2005a). Crack motion in viscoelastic solids: The role of the flash temperature. The European Physical Journal E-Soft Matter, 17(3), 261.
Carbone, G., & Persson, B. N. J. (2005b). Hot cracks in rubber: Origin of the giant toughness of rubber-like materials. Physical Review Letters, 95, 114301.
Carbone, G., & Pierro, E. (2012a). Sticky bio-inspired micropillars: Finding the best shape. Small, 8(9), 1449–1454.
Carbone, G., & Pierro, E. (2012b). Effect of interfacial air entrapment on the adhesion of bio-inspired mushroom-shaped micro-pillars. Soft Matter, 8(30), 7904–7908.
Carbone, G., & Putignano, C. (2013). A novel methodology to predict sliding/rolling friction in viscoelastic materials: Theory and experiments. Accepted on Journal of Mechanics and Physics of Solids.
Carbone, G., Scaraggi, M., & Tartaglino, U. (2009). Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories. The European Physical Journal E-Soft Matter, 30(1), 65–74.
Carbone, G. (2009). A slightly corrected Greenwood and Williamson model predicts asymptotic linearity between contact area and load. Journal of the Mechanics and Physics of Solids, 57(7), 1093–1102.
Carbone, G., & Bottiglione, F. (2008). Asperity contact theories: Do they predict linearity between contact area and load? Journal of the Mechanics and Physics of Solids, 56, 2555–2572.
Carbone, G., & Mangialardi, L. (2004). Adhesion and friction of an elastic half-space in contact with a slightly wavy rigid surface. Journal of the Mechanics and Physics of Solids, 52(6), 1267–1287.
Carbone, G., & Mangialardi, L. (2008a). Analysis of the adhesive contact of confined layers by using a Green’s function approach. Journal of the Mechanics and Physics of Solids, 56, 684–706.
Carbone, G., & Mangialardi, L. (2008b). Analysis of adhesive contact of confined layers by using a Green’s function approach. The Journal of the Mechanics and Physics of Solids, 56(2), 684–706.
Carbone, G., & Putignano, C. (2014). Rough viscoelastic sliding contact: Theory and experiments. Physical Review E, 89, 032408.
Carbone, G., Mangialardi, L., & Persson, B. N. J. (2004). Adhesion between a thin elastic plate, and a hard randomly rough substrate. Physical Review B, 70(12), 125–407.
Carbone, G., Lorenz, B., Persson, B. N. J., & Wohlers, A. (2009). Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties. European Physical Journal E, 29, 275–284.
Carbone, G., Pierro, E., & Gorb, S. (2011). Origin of the superior adhesive performance of mushroom shaped microstructured surfaces. Soft Matter, 7(12), 5545–5552.
Cattaneo, C. (1938). Sul contatto di due corpi elastici: distribuzione locale degli sforzi. Rend. Accad. Naz. Lincei, 27, 342–348, 434–436, 474–478 (in Italian).
Christensen, R. M. (1982). Theory of viscoelasticity. New York: Academic Press.
Ciavarella, M. (1998a). The generalized Cattaneo partial slip plane contact problem I-Theory, II-Examples. International Journal of Solids and Structures, 35, 2349–2378.
Ciavarella, M. (1998b). Tangential loading of general three-dimensional contacts. ASME Journal of Applied Mechanics, 65, 998–1003.
Ciavarella, M., Delfine, V., & Demelio, G. (2006). A “re-vitalized" Greenwood and Williamson model of elastic contact between fractal surfaces. Journal of the Mechanics and Physics of Solids, 54, 2569–2591.
Ciavarella, M., Dibello, S., & Demelio, G. (2008). Conductance of rough random profiles. International Journal of Solids and Structures, 45, 879–893.
D’Amico, F., Carbone, G., Foglia, M. M., & Galietti, U. (2012). Moving cracks in viscoelastic materials: Temperature and energy-release-rate measurements. Engineering Fracture Mechanics (submitted).
Dapp, W. B., Lucke, A., Persson, B. N. J., & Muser, M. H. (2012). Self-affine elastic contacts: Percolation and leakage. Physical Review Letter, 108, 244301.
de Vicente, J., Stokes, J. R., & Spikes, H. R. (2006). Rolling and sliding friction in compliant, lubricated contact. Proceedings Institutions of Mechanical Engineering Part J: Journal of Engineering Tribology, 220.
Derjaguin, B. V., Muller, V. M., & Toporov, Y. P. (1975). Effect of contact deformations on the adhesion of particles. Journal of Colloid and Interface Science, 53, 314–326.
Dieker, A. B., & Mandjes, M. (2003). On spectral simulation of fractional Brownian motion. Probability in the Engineering and Informational Sciences, 17, 417–434.
Eid, H., Adams, G., McGruer, N., Fortini, A., Buldyrev, S., & Srolovitz, D. (2011). A combined molecular dynamics and finite element analysis of contact and adhesion of a rough sphere and a flat surface. Tribology Transactions, 54, 920–928.
Elsharkawy, A. A. (1996). Visco-elastohydrodynamic lubrication of line contacts. Wear, 199, 45–53.
Endlein, T., Barnes, W. J. P., Samuel, D. S., Crawford, N. A., Biaw, A. B., & Grafe, U. (2013). Sticking under wet conditions: The remarkable attachment abilities of the torrent frog. Staurois guttatus, PLoS ONE, 8, e73810.
Eriten, M., Polycarpou, A. A., & Bergman, L. A. (2011). Surface roughness effects on energy dissipation in fretting contact of nominally flat surfaces. ASME Journal Applied Mechanics, 78.
Esfahanian, M., & Hamrock, B. J. (1991). Fluid-film lubrication regimes revisited. Tribology Transactions, 34(4), 628–632.
Felhõs, D., Xu, D., Schlarb, A. K., Váradi, K., & Goda, T. (2008). Viscoelastic characterization of an EPDM rubber and finite element simulation of its dry rolling friction. Express Polymer Letters, 2(3), 157–164.
Ferry, J. D. (1980). Viscoelastic properties of polymers. Wiley, Inc.
Fuller, K. N. G., & Tabor, D. (1975a). The effect of surface roughness on the adhesion of elastic solids. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 345, 327–342.
Fuller, K. N. G., & Tabor, D. (1975b). The effect of surface roughness on the adhesion of elastic solids. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 345(1642), 327–342.
Geike, T., & Popov, V. L. (2007). Mapping of three-dimensional contact problems into one dimension. Physical Review E, 76, 036710.
Geim, A. K., Dubonos, S. V., Gricorieva, I. V., Novoselov, K. S., Zhukov, A. A., & Shapoval, S. Y. (2003a). Microfabricated adhesive mimicking gecko foot-hair. Nature Materials, 2, 461–463.
Geim, A. K., Dubonos, S. V., Gricorieva, I. V., Novoselov, K. S., Zhukov, A. A., & Shapoval, S. Y. (2003b). Microfabricated adhesive mimicking gecko foot-hair. Nature Materials, 2, 461–463.
Greenwood, J. (1997). Adhesion of elastic spheres. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 453, 1277–1297.
Greenwood, J. A. (2006). A simplified elliptic model of rough surface contact. Wear, 261, 191–200.
Greenwood, J. A., & Williamson, J. B. P. (1966). Contact of nominally flat surfaces. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 295, 300–319.
Greenwood, J. A., Putignano, C., & Ciavarella, M. (2011). A Greenwood & Williamson theory for line contact. Wear, 270, 332–334.
Grosch K. A. (1963). The relation between the friction and visco-elastic properties of rubber. Proceedings of the Royal Society of London. Series A: Mathematical and Physical, 274(1356), 21–39.
Hamrock, B. J., Schmid, S. R., & Jacobson, B. O. (2004). Fundamentals of fluid film lubrication. CRC Press.
Harrass, M., Friedrich, K., & Almajid, A. A. (2010). Tribological behavior of selected engineering polymers under rolling contact. Tribology International, 43, 635–646.
Hooke, C. J., & Huang, P. (1997). Elastohydrodynamic lubrication of soft viscoelastic materials in line contact. Proceedings Institutions of Mechanical Engineering Part J: Journal of Engineering Tribology, 211, 185.
Hunter, S. C. (1961). The rolling contact of a rigid cylinder with a viscoelastic half space. Transactions ASME, Series E, Journal of Applied Mechanics, 28, 611–617.
Hutt, W., & Persson, B. N. J. (2016). Soft matter dynamics: Accelerated fluid squeeze-out during slip. The Journal of Chemical Physics, 144, 124903.
Hyun, S., & Robbins, M. O. (2007). Elastic contact between rough surfaces: Effect of roughness at large and small wavelengths. Tribology International, 40, 413–1422.
Hyun, S., Pei, L., Molinari, J.-F., & Robbins, M. O. (2004). Finite-element analysis of contact between elastic self-affine surfaces. Physical Review E, 70, 026117.
Jager, J. (1998). A new principle in contact mechanics. ASME Journal of Tribology, 120, 677–684.
Jang, H., & Barber, J. R. (2011). Effect of phase on the frictional dissipation in systems subjected to harmonically varying loads. European Journal Mechanics A/Solids, 30, 269–274.
Johnson, K. L. (1961). Energy dissipation at spherical surfaces in contact transmitting oscillating forces. Journal of Mechanical Engineering Science, 3, 362–368.
Johnson, K. L. J. (1985). Contact mechanics. Cambridge University Press.
Johnson, K. L., Kendall, K., & Roberts, A. D. (1971). Surface energy and the contact of elastic solids. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 324, 301–313.
Kessler, M. (2004). Advanced topics in characterization of composites. Trafford Publishing.
Krick, B. A., Vail, J. R., Persson, B. N. J., & Sawyer, W. G. (2012). Optical in situ micro tribometer for analysis of real contact area for contact mechanics, adhesion, and sliding experiments. Tribology Letters.
Le Tallec, P., & Rahler, C. (1994). Numerical models of steady rolling for non-linear viscoelastic structures in finite deformations. International Journal for Numerical Methods in Engineering, 37, 1159–1186.
Lorenz, B., & Persson, B. N. J. (2010a). Leak rate of seals: Effective-medium theory and comparison with experiment. European Physical Journal E, 31(2), 159–167.
Lorenz, B., & Persson, B. N. J. (2010b). Time-dependent fluid squeeze-out between solids with rough surfaces. European Physical Journal E, 32(3), 281–290.
Lorenz, B., & Persson, B. N. J. (2010c). On the dependence of the leak rate of seals on the skewness of the surface height probability distribution. EPL, 90, 38002.
Lorenz, B., & Persson, B. N. J. (2009). Interfacial separation between elastic solids with randomly rough surfaces: comparison of experiment with theory. Journal of Physics: Condensed Matter, 21(1), 015003.
Lorenz, B., Persson, B. N. J., Dieluweit, S., & Tada, T. (2011). Rubber friction: Comparison of theory with experiment. European Physical Journal E, 34, 129.
Lorenz, B., Carbone, G., & Schulze, C. (2010). Average separation between solids in rough contact: Comparison between theoretical predictions and experiments. Wear, 268(7–8), 984–990.
Luan, B., & Robbins, M. O. (2009). Hybrid atomistic/continuum study of contact and friction between rough solids. Tribology Letters, 36, 1–16.
Luan, B. Q., Hyun, S., Molinari, J. F., Bernstein, N., & Robbins, M. O. (2006). Multiscale modeling of two-dimensional contacts. Physical Review E, 74, 046710.
Mandelbrot, B. B. (1982). The fractal geometry of nature. New York: W. H. Freeman and company.
Manners, W., & Greenwood, J. A. (2006). Some observations on Persson’s diffusion theory of elastic contact. Wear, 261, 600–610.
Martina, D., Creton, C., Damman, P. M., Jeusette, & Lindner. A., (2012). Adhesion of soft viscoelastic adhesives on periodic rough surfaces. Soft Matter, 8(19), 5350–5357.
Marx, N., Guegan, J., & Spikes, H. A. (2016). Elastohydrodynamic film thickness of soft EHL contacts using optical interferometry. Tribology International, 99, 267–277.
Maugis, D. (1992). Adhesion of spheres: The JKR-DMT transition using a dugdale model. Journal of Colloid and Interface Science, 150, 243–269.
Maugis, D. (1996). On the contact and adhesion of rough surfaces. Journal of Adhesion Science and Technology, 10, 161–175.
Medina, S., & Dini, D. (2014). A numerical model for the deterministic analysis of adhesive rough contacts down to the nano-scale. International Journal of Solids and Structures, 51, 2620–2632.
Mindlin, R. D. (1949). Compliance of elastic bodies in contact. ASME Journal of Applied Mechanics, 16, 259–268.
Mser, M. H., Dapp, W. B., Bugnicourt, R., Sainsot, P., Lesaffre, N., Lubrecht, A. A., et al. (2017). Meeting the contact-mechanics challenge. Tribology Letters, 65, 118.
Muller, V., Yushchenko, V., & Derjaguin, B. (1980). On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. Journal of Colloid and Interface Science, 77, 91–101.
Munisamy, R. L., Hills, D. A., & Nowell, D. (1994). Static axisymmetrical Hertzian contacts subject to shearing forces. ASME Journal of Applied Mechanics, 61, 278–283.
Nackenhorst, U. (2004). The ALE-formulation of bodies in rolling contact Theoretical foundations and finite element approach. Computer Methods in Applied Mechanics and Engineering, 193, 4299–4322.
Nasdala, L., Kaliske, M., Becker, A., & Rothert, H. (1998). An efficient viscoelastic formulation for steady-state rolling structures. Computational Mechanics, 22, 395–403.
Nowell, D., Dini, D., & Hills, D. A. (2006). Recent developments in the understanding of fretting fatigue. Engineering Fracture Mechanics, 73, 207–222.
O’Boy, D. J., & Dowling, A. P. (2009). Tyre/road interaction noise–A 3D viscoelastic multilayer model of a tyre belt. Journal of Sound and Vibration, 322(4–5), 829–850.
Olaru, D. N., Stamate, C., & Prisacaru, G. (2009). Rolling friction in a micro tribosystem. Tribology Letters, 35, 205–210.
Padovan, J. (1987). Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure-I. Theory. Computers & Structures, 27(2), 249–257.
Padovan, J., & Paramadilok, O. (1984). Transient and steady state viscoelastic rolling contact. Computers & Structures, 20, 545–553.
Padovan, J., Kazempour, A., Tabaddor, F., & Brockman, B. (1992). Alternative formulations of rolling contact problems. Finite Elements in Analysis and Design, 11, 275–284.
Paggi, M., & Barber, J. R. (2011). Contact conductance of rough surfaces composed of modified RMD patches. International Journal of Heat and Mass Transfer, 54(21–22), 4664–4672.
Paggi, M., & Ciaveralla, M. (2010). The coefficient of proportionality k between real contact area and load, with new asperity models. Wear, 268, 1020–1029.
Pandey, A., Karpitschka, S., Venner, C. H., & Snoeijer, J. H. (2016). Lubrication of soft viscoelastic solids. Journal of Fluid Mechanics, 799, 433–447.
Panek, C., & Kalker, J. J. (1980). Three-dimensional contact of a rigid roller traversing a viscoelastic half space. IMA Journal of Applied Mathematics, 26, 299–313.
Pastewka, L., & Robbins, M. O. (2014). Contact between rough surfaces and a criterion for macroscopic adhesion. Proceedings of the National Academy of Sciences, 111, 3298–3303.
Persson, B. N. J. (2006a). Contact mechanics for randomly rough surfaces. Surface Science Reports, 61, 201–227.
Persson, B. N. J. (2006b). Rubber friction: Role of the flash temperature. Journal of Physics Condensed Matter, 18(32), 7789–7823.
Persson, B. N. J., & Brener, E. A. (2005). Crack propagation in viscoelastic solids. Physical Review E, 71(3), 036123.
Persson, B. N. J., Albohr, O., Heinrich, G., & Ueba, H. (2005). Crack propagation in rubber-like materials. Journal of Physics-Condensed Matter, 17(44), R1071–R114.
Persson, B. N. J. (2001). Theory of rubber friction and contact mechanics. Journal of Chemical Physics, 115, 3840–3861.
Persson, B. N. J. (2010). Rolling friction for hard cylinder and sphere on viscoelastic solid. European Physical Journal E, 33, 327–333.
Persson, B. N., & Scaraggi, M. (2014). Theory of adhesion: Role of surface roughness. The Journal of Chemical Physics, 141, 124701.
Persson, B. N., & Tosatti, E. (2001). The effect of surface roughness on the adhesion of elastic solids. The Journal of Chemical Physics, 115, 5597–5610.
Persson, B. N. J., Bucher, F., & Chiaia, B. (2002). Elastic contact between randomly rough surfaces: Comparison of theory with numerical results. Physical Review B, 65, 184106.
Persson, B. N. J., Lorenz, B., & Volokitin, A. I. (2010). Heat transfer between elastic solids with randomly rough surfaces. European Physics Journal E, 31, 3–24.
Putignano, C., Afferrante, L., Carbone, G., & Demelio, G. (2012a). The influence of the statistical properties of self-affine surfaces in elastic contact: A numerical investigation. Journal of Mechanics and Physics of Solids, 60(5), 973–982.
Putignano, C., Afferrante, L., Carbone, G., & Demelio, G. (2012b). A new efficient numerical method for contact mechanics of rough surfaces. International Journal of Solids and Structures, 49(2), 338–343.
Putignano, C., & Dini, D. (2017). Soft matter lubrication: Does solid viscoelasticity matter? ACS Applied Materials & Interfaces, 9(48), 42287–42295.
Putignano, C., Ciavarella, M., & Barber, J. R. (2011). Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying load. Journal of Mechanics and Physics of Solids, 59(12), 2442–2454.
Putignano, C., Reddyhoff, T., Dini, D., & Carbone, G. (2013). The effect of viscoelasticity in rolling contacts: A combined experimental and numerical investigation. Tribology Letters, 51(1), 105–113.
Putignano, C., Le Rouzic, J., Reddyhoff, T., Carbone, G., & Dini, D. (2014). A theoretical and experimental study of viscoelastic rolling contacts incorporating thermal effects. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 228(10), 1112–1121.
Putignano, C., Carbone, G., & Dini, D. (2015). Mechanics of rough contacts in elastic and viscoelastic thin layers. International Journal of Solids and Structures, 69, 507–517.
Rao, J. S. (2011). Finite element methods, history of mechanism and machine. Science, 20, 141–183.
Sauer, R. A., & Wriggers, P. (2009). Formulation and analysis of a three-dimensional finite element implementation for adhesive contact at the nanoscale. Computer Methods in Applied Mechanics and Engineering, 198, 3871–3883.
Scaraggi M., Putignano C., & Carbone G. (2013). Elastic contact of rough surfaces: A simple criterion to make 2D isotropic roughness equivalent to 1D one. Wear, 297 (1–2, 5), 811–817.
Scaraggi, M., Carbone, G., Persson, B. N. J., & Dini, D. (2011). Mixed lubrication in soft contacts: A novel homogenized approach. Part I-Theory. Soft Matter, 7(21), 1039510406.
Scaraggi, M., Carbone, G., & Dini, D. (2011). Experimental evidence of micro-EHL lubrication in rough soft contacts. Tribology Letters, 43(2), 169–174.
Schenk, O., & Gärtnerc, K. (2004). Solving unsymmetric sparse systems of linear equations with PARDISO. Future Generation Computer Systems, 20(3), 475–487.
Selway, N., Chana, V., & Stokes, J. R. (2017). Influence of fluid viscosity and wetting on multiscale viscoelastic lubrication in soft tribological contacts. Soft Matter, 8.
Sevostianov, I., & Kachanov, M. (2008). Normal and tangential compliances of interface of rough surfaces with contacts of elliptic shape. International Journal of Solids and Structures, 45, 2723–2736.
Snoeijer, J. H., Eggers, J., & Venner, C. H. (2013). Similarity theory of lubricated Hertzian contacts. Physics of Fluids, 25(10), 101705.
Stupkiewicz, S., Lengiewicz, J., Sadowski, P., & Kucharski, S. (2016). Finite deformation effects in soft elastohydrodynamic lubrication problems. Tribology International, 511–522, 93.
Tabor, D. (1977). Surface forces and surface interactions. Journal of Colloid and Interface Science, 58, 2–13.
Thomas, T. R. (1982). Rough surfaces (chap. 8). New York: Longman Group Limited.
Vakis, A. I., Yastrebov, V. A., Scheibert, J., Nicola, L., Dini, D., Minfray, C., et al. (2018). Modeling and simulation in tribology across scales: An overview. Tribology International, 125(2018), 169–199.
Venner, C. H., & Lubrecht, A. A. (2000). Multilevel methods in lubrication. Elsevier Tribology Series (Ed. D. Dowson et al., Vol. 37).
Vollebregt, E. A. H. (2009). User guide for contact, J.J. Kalker’s variational contact model. Technical Report TR09-03, version 1.18.
Wentzel, H. (2006). Modelling of frictional joints in dynamically loaded structures: A review. Technical Report, KTH Solid mechanics, Royal Institute of Technology www.old.hallf.kth.se/forskning/publikationer/rapport_419.pdfS.
Williams, J. R., & O’Connor, R. (1999). Discrete element simulation and the contact problem. Archives of Computational Methods in Engineering, 6(4), 279–304.
Wriggers, P. (2002). Computational contact mechanics. Chichester: Wiley & Sons Ltd.
Yang, C., & Persson, B. N. J. (2008). Molecular dynamics study of contact mechanics: Contact area and interfacial separation from small to full contact. Physical Review Letters, 100, 024303.
Yang, C., Tartaglino, U., & Persson, B. N. J. (2006). A multiscale molecular dynamics approach to contact mechanics. The European Physical Journal E Soft-Matter, 19(1), 47–58.
Yoneyama, S., Gotoh, J., & Takashi, M. (2010). Experimental analysis of rolling contact stresses in a viscoelastic strip, 40(2), 203–210.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 CISM International Centre for Mechanical Sciences
About this chapter
Cite this chapter
Putignano, C., Dini, D. (2020). Contact Mechanics of Rubber and Soft Matter. In: Paggi, M., Hills, D. (eds) Modeling and Simulation of Tribological Problems in Technology. CISM International Centre for Mechanical Sciences, vol 593. Springer, Cham. https://doi.org/10.1007/978-3-030-20377-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-20377-1_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20376-4
Online ISBN: 978-3-030-20377-1
eBook Packages: EngineeringEngineering (R0)