Skip to main content
SpringerLink
Log in

Optimal Energy Dissipation in Sliding Friction Simulations

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

Non-equilibrium molecular dynamics simulations, of crucial importance in sliding friction, are hampered by arbitrariness and uncertainties in the removal of the frictionally generated Joule heat. Building upon general pre-existing formulation, we implement a fully microscopic dissipation approach which, based on a parameter-free, non-Markovian, stochastic dynamics, absorbs Joule heat equivalently to a semi-infinite solid, and harmonic substrate. As a test case, we investigate the stick–slip friction of a slider over a two-dimensional Lennard-Jones solid, comparing our virtually exact frictional results with approximate ones from commonly adopted dissipation schemes. Remarkably, the exact results can be closely reproduced by a standard Langevin dissipation scheme, once its parameters are determined according to a general and self-standing variational procedure.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. The correlated random noise sequence, to be applied to the boundary layer atoms, has been generated at the beginning of the simulation using the rules (15). If we have to correlate in time a single random number sequence, we can generate a set of uncorrelated numbers in Fourier space, multiply them by the Fourier transform of the correlation matrix and make the inverse transform to get back to the real space [19].

References

  1. Persson, B.N.J.: Sliding Friction. Springer, Berlin (1998)

    Google Scholar 

  2. Robbins, M.O., Müser, M.H.: Computer simulations of friction, lubrication, and wear. In: Bhushan, B. (ed.) Modern Tribology Handbook Vol. I. CRC Press, New York (2001)

    Google Scholar 

  3. Vanossi, A., Manini, N., Urbakh, M., Zapperi, S., Tosatti, E.: Modeling friction: from nano to meso scales. Sub. Rev. Mod. Phys. (2012) p. arXiv:1112.3234v1

  4. Li, Q., Dong, Y., Perez, D., Martini, A., Carpick, R.W.: Speed dependence of atomic stick-slip friction in optimally matched experiments and molecular dynamics simulations. Phys. Rev. Lett. 106(1), 126101–00 (2011)

    Google Scholar 

  5. Zwanzig, R.: Nonequilibrium statistical mechanics. Oxford University Press, New York (2001)

    Google Scholar 

  6. Medyanik, S.N., Liu, W.K., Sung, I.-H., Carpick, R.W.: Predictions and observations of multiple slip modes in atomic-scale friction. Phys. Rev. Lett. 97, 136106 (2006)

    Article  Google Scholar 

  7. Benassi, A., Vanossi, A., Santoro, G.E., Tosatti, E.: Parameter-free dissipation in simulated sliding friction. Phys. Rev. B 82, 081401(R) (2010)

  8. Maradudin, A.A., Montroll, E.W., Weiss, G.H., Ipatova, I.P.: Theory of lattice dynamics in the harmonic approximation. In: Solid State Physics, Academic Press, New York (1971)

  9. Rubin, R.J.: Statistical dynamics of simple cubic lattices. Model for the study of brownian motion. J. Math. Phys. 1, 309 (1960)

    Article  Google Scholar 

  10. Campana, C., Müser, M.H.: Practical greens function approach to the simulation of elastic semi-infinite solids. Phys. Rev. B 74, 075420 (2006)

    Article  Google Scholar 

  11. Luan, B.Q., Hyun, S., Molinari, J.F., Bernstein, N., Robbins, M.O.: Multiscale modeling of two-dimensional contacts. Phys. Rev. E 74, 046710 (2006)

    Article  CAS  Google Scholar 

  12. Zwanzig, R.: On the identity of three generalized master equations. Physica 30, 1109 (1964)

    Article  Google Scholar 

  13. Mori, H.: Transport, collective motion, and brownian motion. Prog. Theor. Phys. 33, 423 (1965)

    Article  Google Scholar 

  14. Evstigneev, M., Reimann, P.: Langevin equation for a system nonlinearly coupled to a heat bath. Phys. Rev. B 82, 224303 (2010)

    Article  Google Scholar 

  15. Magalinskii, V.B: Dynamical model on the theory of the (quantum) Brownian motion. Sov. Phys. JETP 9, 1381 (1959)

    Google Scholar 

  16. Li, X., E, W.: Variational boundary conditions for molecular dynamics simulations of crystalline solids at finite temperature: Treatment of the thermal bath. Phys. Rev. B 76, 104107 (2007)

    Article  Google Scholar 

  17. Kantorovich, L.: Generalized Langevin equation for solids. I. Rigorous derivation and main properties. Phys. Rev. B 78, 094304 (2008)

    Article  Google Scholar 

  18. Kantorovich, L., Rompotis, N.: Generalized Langevin equation for solids. II. Stochastic boundary conditions for nonequilibrium molecular dynamics simulations. Phys. Rev. B 78, 094305 (2008)

    Article  Google Scholar 

  19. Lü, K., Bao, J.-D.: Numerical simulation of generalized Langevin equation with arbitrary correlated noise. Phys. Rev. E 72, 067701 (2005)

    Article  Google Scholar 

  20. Vanossi, A., Braun, O.M.: Driven dynamics of simplified tribological models. J. Phys. Cond. Mat. 19, 305017 (2007)

    Article  Google Scholar 

  21. Braun, O., Naumovets, A.: Nanotribology: microscopic mechanisms of friction. Surf. Sci. Rep. 60, 79 (2006)

    Article  CAS  Google Scholar 

  22. Luan, B.Q., Robbins, M.O.: Hybrid atomistic/continuum study of contact and friction between rough solids. Trib. Lett. 36, 1 (2009)

    Article  CAS  Google Scholar 

Download references

Acknowledgments

A discussion with L. Kantorovich is gratefully acknowledged. This study is part of Eurocores Projects FANAS/AFRI, sponsored by the Italian Research Council (CNR), and of FANAS/ACOF. It is also sponsored by the Italian PRIN Contracts No. 20087NX9Y7 and No. 2008Y2P573, and by the Swiss National Science Foundation SINERGIA Project CRSII2 136287\ 1.

Author information

Authors and Affiliations

  1. CNR Istituto per l’Energetica e le Interfasi (CNR-IENI), Via Cozzi 53, 20125, Milano, Italy

    A. Benassi

  2. Centro S3, CNR Istituto Nanoscienze, Via Campi 213/A, 41125, Modena, Italy

    A. Benassi

  3. International School for Advanced Studies (SISSA), Via Bonomea 265, 34136, Trieste, Italy

    A. Vanossi, G. E. Santoro & E. Tosatti

  4. CNR-IOM Democritos National Simulation Center, Via Bonomea 265, 34136, Trieste, Italy

    A. Vanossi, G. E. Santoro & E. Tosatti

  5. International Centre for Theoretical Physics (ICTP), P.O. Box 586, 34014, Trieste, Italy

    G. E. Santoro & E. Tosatti

Authors
  1. A. Benassi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Vanossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. E. Santoro
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. Tosatti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Benassi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Benassi, A., Vanossi, A., Santoro, G.E. et al. Optimal Energy Dissipation in Sliding Friction Simulations. Tribol Lett 48, 41–49 (2012). https://doi.org/10.1007/s11249-012-9936-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11249-012-9936-5

Keywords

Search

Navigation