Skip to main content
SpringerLink
Log in

Reliability of Micromechanical Contact Models: a Still Open Issue

  • Chapter
Book cover Computational Contact Mechanics

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 498))

  • 2095 Accesses

Abstract

The assumption of perfectly flat surfaces within the context of the contact problems constitutes very often an oversimplification of the reality. In fact, when real surfaces are examined more in details, roughness can be found at different scale lengths. This fundamental feature poses enormous difficulties on the mathematical modeling of the physics of the contact problems. Nevertheless, the study of the effect of the multiscale roughness on the contact predictions is crucial from the engineering point of view. To deal with this problem several micromechanical contact models have been developed since the middle of the 19th Century. Such models are based on very different mathematical frameworks, with a consequent lack of standardization. The recent perspective to apply such models to smaller and smaller scale lengths, down to the nanoscale, makes the reliability of these models a still open issue. The basic aim of this chapter is to provide a detailed review of the most popular contact models available in the literature. Moreover we focus one the crucial intent of providing a degree of confidence about the differences between the contact predictions provided by the models. For this purpose a critical comparison of the outcomes of such models by applying them to numerically generated rough surfaces is then proposed.

The financial support of the European Union to the Leonardo da Vinci Project I/06/B/F/PP-154069 “Innovative Learning and Training on Fracture (ILTOF)” and of the Italian Ministry of University and Research to the project PRIN2005 “Modelling and approximation in advanced mechanical problems” is gratefully acknowledged.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • G.G. Adams and S. Müftü. Improvements to a scale-dependent model for contact and friction. International Journal of Physics D, 38:1402–1409, 2005.

    Article  Google Scholar 

  • G.G. Adams, S. Müftü, and N.M. Azhar. A scale-dependent model for multi-asperity contact and friction. ASME Journal of Tribology, 125:700–708, 2003.

    Article  Google Scholar 

  • G. Amontons. De la resistance causée dans les machines. Mémoires de l’Académie Royale, pages 257–282, 1699.

    Google Scholar 

  • J.F. Archard. Elastic deformation and the laws of friction. Proceedings of the Royal Society of London, Ser. A, 243:190–205, 1957.

    Article  Google Scholar 

  • J.R. Barber. Bounds on the electrical resistance between contacting elastic rough bodies. Proceedings of the Royal Society of London, Ser. A, 459:53–66, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  • M. Borri-Brunetto, A. Carpinteri, and B. Chiaia. Scaling phenomena due to fractal contact in concrete and rock fractures. International Journal of Fracture, 95:221–238, 1999a.

    Article  Google Scholar 

  • M. Borri-Brunetto, A. Carpinteri, and B. Chiaia. Scaling phenomena due to fractal contact in concrete and rock fractures. International Journal of Fracture, 95:221–238, 1999b.

    Article  Google Scholar 

  • M. Borri-Brunetto, B. Chiaia, and M. Paggi. Multiscale models for contact mechanics of rough surfaces. In R. Buzio and U. Valbusa, editors, Chapter 1 in Advances in Contact Mechanics: Implications for Materials Science, Engineering & Biology, pages 1–41. Research Signpost, Trivandrum (India), 2006.

    Google Scholar 

  • E. Bouchaud. Scaling properties of cracks. Journal of Physics: Condensed Matter, 9:4319–4344, 1997.

    Article  Google Scholar 

  • F.P. Bowden and D. Tabor. The Friction and Lubrication of Solids, Part II. Clarendon Press, Oxford, 1964.

    Google Scholar 

  • H. Buckle. Use of hardness test to determine other material properties. In J.H. Westerbrook and H. Conrad, editors, The Science of Hardness Testing and its Research Applications, pages 453–494. American Society of Metals, Metals Park, OH, 1973.

    Google Scholar 

  • A.W. Bush, R.D. Gibson, and G.P. Keogh. The limit of elastic deformation in the contact of rough surfaces. Mechanical Resources Communications, 3:169–174, 1976.

    Article  Google Scholar 

  • A.W. Bush, R.D. Gibson, and G.P. Keogh. Strongly anisotropic rough surfaces. American Society of Mechanical Engineers, 78-LUB-16, 1978.

    Google Scholar 

  • R. Buzio, C. Boragno, F. Biscarini, F. Buatier de Mongeot, and U. Valbusa. The contact mechanics of fractal surfaces. Nature Materials, 2:233–236, 2003.

    Article  Google Scholar 

  • A. Carpinteri. Scaling laws and renormalization groups for strength and toughness of disordered materials. International Journal of Solids and Structures, 31:291–302, 1994a.

    Article  MATH  Google Scholar 

  • A. Carpinteri. Fractal nature of material microstructure and size effects on apparent mechanical properties. Mechanics of Materials, 18:89–101, 1994b. Internal Report, Laboratory of Fracture Mechanics, Politecnico di Torino, N. 1/92, 1992.

    Article  Google Scholar 

  • A. Carpinteri and B. Chiaia. Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy. RILEM Materials & Structures, 28:435–443, 1995.

    Article  Google Scholar 

  • A. Carpinteri and M. Paggi. Size-scale effects on the friction coefficient. International Journal of Solids and Structures, 42:2901–2910, 2005.

    Article  MATH  Google Scholar 

  • A. Carpinteri and M. Paggi. A fractal interpretation of size-scale effects on strength, friction and fracture energy of faults. Chaos, Solitons & Fractals, 2007. doi:10.1016/j.chaos.2007.01.075.

    Google Scholar 

  • A. Carpinteri, M. Paggi, and G. Zavarise. Snap-back instability in micro-structured composites and its connection with superplasticity. Strength, Fracture and Complexity, 3:61–72, 2005.

    Google Scholar 

  • D.E. Cartwright and M.S. Longuet-Higgins. The distribution of the maxima of a random function. Philosophycal Transaction of the Royal Society of London, Ser.A, 237:212–232, 1956.

    MATH  MathSciNet  Google Scholar 

  • W.R. Chang, I. Etsion, and D.B. Bogy. An elastic-plastic model for the contact of rough surfaces. ASME Journal of Tribology, 109:257–263, 1987.

    Article  Google Scholar 

  • M. Ciavarella and G. Demelio. Elastic multiscale contact of rough surfaces: Archard’s model revisited and comparisons with modern fractal models. ASME Journal of Applied Mechanics, 68:496–498, 2001.

    Article  MATH  Google Scholar 

  • M. Ciavarella, G. Demelio, J.R. Barber, and Y.H. Jang. Linear elastic contact of the Weierstrass profile. Proceedings of the Royal Society of London, Ser. A, 456:387–405, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  • M.G. Cooper, B.B. Mikic, and M.M. Yovanovich. Thermal contact conductance. International Journal of Heat and Mass Transfer, 12:279–300, 1968.

    Article  Google Scholar 

  • J. Feder. Fractals. Plenum Press, New York, 1988.

    MATH  Google Scholar 

  • W. Feller. Probability Theory and its Applications, 2nd ed. Wiley, New York, 1971.

    MATH  Google Scholar 

  • I. Green. A transient dynamic analysis of mechanical seals including asperity contact and face deformation. Tribology Transactions, 45:284–293, 2002.

    Article  Google Scholar 

  • J.A. Greenwood. A unified theory of surface roughness. Proceedings of the Royal Society of London, Ser. A, 393:133–157, 1984.

    Article  Google Scholar 

  • J.A. Greenwood and J.H. Tripp. The contact of two nominally flat rough surfaces. Proc. Instn. Mech. Engrs., Part J, 185:625–633, 1971.

    Article  Google Scholar 

  • J.A. Greenwood and J.B.P. Williamson. Contact of nominally flat surfaces. Proceedings of the Royal Society of London, Ser. A, 295:300–319, 1966.

    Article  Google Scholar 

  • J.A. Greenwood and J.J. Wu. Surface roughness and contact: an apology. Meccanica, 36:617–630, 2001.

    Article  MATH  Google Scholar 

  • A.A.H. Hegazy. Thermal Joint Conductance of Conforming Rough Surfaces; Effect of Surface Micro-Hardness Variation. PhD thesis, University of Waterloo, 1985.

    Google Scholar 

  • K.L. Johnson. Contact Mechanics. Cambridge University Press, Cambridge, 1985.

    MATH  Google Scholar 

  • L. Kogut and I. Etsion. A finite element based elastic-plastic model for the contact of rough surfaces. Tribology Transactions, 46:383–390, 2003.

    Article  Google Scholar 

  • M.S. Longuet-Higgins. The statistical analysis of a random moving surface. Philosophycal Transaction of the Royal Society of London, Ser.A, 249:321–387, 1957a.

    Article  MATH  MathSciNet  Google Scholar 

  • M.S. Longuet-Higgins. Statistical properties of an isotropic random surface. Philosophycal Transaction of the Royal Society of London, Ser.A, 250:157–174, 1957b.

    Article  MATH  MathSciNet  Google Scholar 

  • A. Majumdar and B. Bhushan. Role of fractal geometry in roughness characterization and contact mechanics of surfaces. ASME Journal of Tribology, 112:205–216, 1990.

    Article  Google Scholar 

  • A. Majumdar and B. Bhushan. Fractal model of elastic-plastic contact between rough surfaces. ASME Journal of Tribology, 113:1–11, 1991.

    Article  Google Scholar 

  • B.B. Mandelbrot, D.E. Passoja, and A.J. Paullay. Fractal character of fractal surfaces of metals. Nature, 308:721–722, 1984.

    Article  Google Scholar 

  • J.I. McCool. Comparison of models for the contact of rough surfaces. Wear, 107:37–60, 1986.

    Article  Google Scholar 

  • D. Middleton. An Introduction to Statistical Communication Theory. McGraw-Hill, New York, 1960.

    Google Scholar 

  • B.B. Mikic. Thermal contact conductance: theoretical considerations. International Journal of Heat and Mass Transfer, 205:416–417, 1974.

    Google Scholar 

  • P.R. Nayak. Random process model of rough surfaces. ASME Journal of Lubrication Technology, 93:398–407, 1971a.

    Google Scholar 

  • P.R. Nayak. Random process model of rough surfaces in plastic contact. Wear, 26:305–333, 1973.

    Article  Google Scholar 

  • P.R. Nayak. Random process model of rough surfaces. ASME Journal of Lubrication Technology, 93:398–407, 1971b.

    Google Scholar 

  • M. Paggi. Interface Mechanical Problems in Heterogeneous Materials. PhD thesis, Politecnico di Torino, Torino, Italy, 2005.

    Google Scholar 

  • M. Paggi, A. Carpinteri, and G. Zavarise. A unified interface constitutive law for the study of fracture and contact problems in heterogeneous materials. In P. Wriggers and U. Nackenhorst, editors, Analysis and Simulation of Contact Problems, Lecture Notes in Applied and Computational Mechanics, volume 27, pages 297–304. Springer-Verlag, Berlin, 2006.

    Chapter  Google Scholar 

  • H.O. Peitgen and D. Saupe. The Science of Fractal Images. Springer-Verlag, New York, 1988.

    MATH  Google Scholar 

  • B.N.J. Persson. Elastoplastic contact between randomly rough surfaces. Physical Review Letters, 87:116101, 1–4, 2001a.

    Article  Google Scholar 

  • B.N.J. Persson. Theory of rubber friction and contact mechanics. Journal of Chemical Physics, 115(8):3840–3861, 2001b.

    Article  Google Scholar 

  • B.N.J. Persson. Adhesion between elastic bodies with randomly rough surfaces. Physical Review Letters, 89:245502, 2002a.

    Article  Google Scholar 

  • B.N.J. Persson. Adhesion between elastic bodies with randomly rough surfaces. European Physical Journal, E8:385, 2002b.

    Google Scholar 

  • B.N.J. Persson, F. Bucher, and B. Chiaia. Elastic contact between randomly rough surfaces: comparison of theory with numerical results. Physical Review B, 65:184106, 1–7, 2002.

    Article  Google Scholar 

  • S.O. Rice. Mathematical analysis of random noise. In N. Wax, editor, Selected Papers on Noise and Stochastic Processes, page 211. Dover Publications Inc., 1954.

    Google Scholar 

  • R.A. Roberts and B.F. Barton. Theory of Signal Detectability: Composite Deferred Decision Theory. University of Michigan, Dep. of Electrical Engineering-Technical Report N. 161, 1965.

    Google Scholar 

  • R.S. Sayles and T.R. Thomas. The spatial representation of surface roughness by means of the structure function: a practical alternative to correlation. Wear, 42:263–276, 1977.

    Article  Google Scholar 

  • R.S. Sayles and T.R. Thomas. Surface topography as a nonstationary random process. Nature, 271:431–434, 1978.

    Article  Google Scholar 

  • M.R. Sridhar and M.M. Yovanovich. Review of elastic and plastic contact conductance models: Comparison with experiments. Journal of Thermophysics and Heat Transfer, 8(4):633–640, 1994.

    Article  Google Scholar 

  • T.R. Thomas and B.-G. Rosén. Determination of the optimum sempling interval for rough contact mechanics. Tribology International, 33:601–610, 2000.

    Article  Google Scholar 

  • E.E. Underwood and K. Banerjee. Fractal analysis of fracture surfaces. In J.H. Westerbrook and H. Conrad, editors, ASM Handbook, vol. 12: Fractography, pages 211–215. ASM International, Metals Park, Ohio, USA, 1987.

    Google Scholar 

  • D. Veneziano. Basic properties and characterization of stochastically self-similar processes in R d. Fractals, 7:59–78, 1998.

    Article  MathSciNet  Google Scholar 

  • K.L. Woo and T.R. Thomas. Contact of rough surfaces: a review of experimental work. Wear, 58:331–340, 1980.

    Article  Google Scholar 

  • P. Wriggers. Computational Contact Mechanics. John Wiley & Sons, Ltd., The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, England, 2002.

    Google Scholar 

  • P. Wriggers and G. Zavarise. Computational contact mechanics. In E. Stein, R. De Borst, and T.J.R. Huges, editors, Encyclopedia of Computational Mechanics, Vol. 2 — Solids and Structures, pages 195–226. John Wiley & Sons Ltd, Chichester, 2004.

    Google Scholar 

  • M.M. Yovanovich, J.W. De Vaal, and A.A. Hegazy. A statistical model to predict thermal gap conductance between conforming rough surfaces. AIAA Paper, 82-0888, 1982.

    Google Scholar 

  • G. Zavarise. Problemi termomeccanici di contatto-Aspetti fisici e computazionali. PhD thesis, Istituto di Scienza e Tecnica delle Costruzioni, University of Padua, Padua, Italy, 1991.

    Google Scholar 

  • G. Zavarise and B.A. Schrefler. Numerical analysis of microscopically elastic contact problems. In M. Raous, M. Jean, and J.J. Moreau, editors, Contact Mechanics, pages 305–312, New York and London, 1995. Plenum Press.

    Google Scholar 

  • G. Zavarise, P. Wriggers, E. Stein, and B.A. Schrefler. A numerical model for thermomechanical contact based on microscopic interface laws. Mechanics and Resource Communications, 19:173–182, 1992a.

    Article  MATH  Google Scholar 

  • G. Zavarise, P. Wriggers, E. Stein, and B.A. Schrefler. Real contact mechanisms and finite element formulation-a coupled thermomechanical approach. International Journal for Numerical Methods in Engineering, 35:767–785, 1992b.

    Article  MATH  Google Scholar 

  • G. Zavarise, M. Borri-Brunetto, and M. Paggi. A comparison of the mechanical behavior of microscopical contact models. In International Conference on Nonsmooth/Nonconvex Mechanics with Applications in Engineering, Thessaloniki, Greece, pages 111–118, 2002.

    Google Scholar 

  • G. Zavarise, M. Borri-Brunetto, and M. Paggi. On the reliability of microscopical contact models. Wear, 257:229–245, 2004.

    Article  Google Scholar 

  • G. Zavarise, M. Borri-Brunetto, and M. Paggi. On the resolution dependence of micromechanical contact models. Wear, 262:42–54, 2007.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Innovation Engineering, University of Salento, Lecce, Italy

    Giorgio Zavarise

  2. Department of Structural and Geotechnical Engineering, Politecnico di Torino, Torino, Italy

    Marco Paggi

Authors
  1. Giorgio Zavarise
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco Paggi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Hannover, Germany

    Peter Wriggers

  2. Duke University, Durham, NC, USA

    Tod A. Laursen

Rights and permissions

Reprints and permissions

Copyright information

© 2007 CISM, Udine

About this chapter

Cite this chapter

Zavarise, G., Paggi, M. (2007). Reliability of Micromechanical Contact Models: a Still Open Issue. In: Wriggers, P., Laursen, T.A. (eds) Computational Contact Mechanics. CISM International Centre for Mechanical Sciences, vol 498. Springer, Vienna. https://doi.org/10.1007/978-3-211-77298-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-211-77298-0_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-77297-3

  • Online ISBN: 978-3-211-77298-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation