Skip to main content
Log in

Shear-strain and shear-stress fluctuations in generalized Gaussian ensemble simulations of isotropic elastic networks

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Shear-strain and shear-stress correlations in isotropic elastic bodies are investigated both theoretically and numerically at either imposed mean shear-stress τ (λ = 0) or shear-strain γ (λ = 1) and for more general values of a dimensionless parameter λ characterizing the generalized Gaussian ensemble. It allows to tune the strain fluctuations \(\mu _{\gamma \gamma } \equiv \beta V\left\langle {\delta \hat \gamma ^2 } \right\rangle = (1 - \lambda )/G_{eq}\) with β being the inverse temperature, V the volume, \(\hat \gamma\) the instantaneous strain and G eq the equilibrium shear modulus. Focusing on spring networks in two dimensions we show, e.g., for the stress fluctuations \(\mu _{\tau \tau } \equiv \beta V\left\langle {\delta \hat \tau ^2 } \right\rangle\) (\(\hat \tau\) being the instantaneous stress) that μ ττ | λ = μ Aλ G eq with μ A = μ ττ | λ = 0 being the affine shear-elasticity. For the stress autocorrelation function \(C_{\tau \tau } (t) \equiv \beta V\left\langle {\delta \hat \tau (t)\delta \hat \tau (0)} \right\rangle\) this result is then seen (assuming a sufficiently slow shear-stress barostat) to generalize to C ττ (t)| λ = G(t) − λ G eq with G(t) = C ττ (t) | λ = 0 being the shear-stress relaxation modulus.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Allen, D. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1994)

  2. J.L. Lebowitz, J.K. Percus, L. Verlet, Phys. Rev. 153, 250 (1967)

    Article  ADS  Google Scholar 

  3. H.B. Callen, Thermodynamics and an Introduction to Thermostatistics (Wiley, New York, 1985)

  4. D. Frenkel, B. Smit, Understanding Molecular Simulation – From Algorithms to Applications, 2nd edn. (Academic Press, San Diego, 2002)

  5. D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2000)

  6. J. Thijssen, Computational Physics (Cambridge University Press, Cambridge, 1999)

  7. M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1954)

  8. J.P. Wittmer, H. Xu, P. Polińska, F. Weysser, J. Baschnagel, J. Chem. Phys. 138, 12A533 (2013)

    Google Scholar 

  9. J.P. Wittmer, H. Xu, J. Baschnagel, Phys. Rev. E 91, 022107 (2015)

    Article  ADS  Google Scholar 

  10. J.P. Wittmer, H. Xu, O. Benzerara, J. Baschnagel, Mol. Phys. (2015), DOI: 10.1080/0268976.2015.1023225

  11. J. Hansen, I. McDonald, Theory of Simple Liquids, 3rd edn. (Academic Press, New York, 2006)

  12. J. Hetherington, J. Low Temp. Phys. 66, 145 (1987)

    Article  ADS  Google Scholar 

  13. M. Costeniuc, R. Ellis, H. Touchette, B. Turkington, Phys. Rev. E 73, 026105 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  14. K. van Workum, J. de Pablo, Phys. Rev. E 67, 011505 (2003)

    Article  ADS  Google Scholar 

  15. T. Witten, P.A. Pincus, Structured Fluids: Polymers, Colloids, Surfactants (Oxford University Press, Oxford, 2004)

  16. M. Rubinstein, R. Colby, Polymer Physics (Oxford University Press, Oxford, 2003)

  17. J.P. Wittmer, H. Xu, P. Polińska, C. Gillig, J. Helfferich, F. Weysser, J. Baschnagel, Eur. Phys. J. E 36, 131 (2013)

    Article  Google Scholar 

  18. D.R. Squire, A.C. Holt, W.G. Hoover, Physica 42, 388 (1969)

    Article  ADS  Google Scholar 

  19. H. Mizuno, S. Mossa, J.-L. Barrat, Phys. Rev. E 87, 042306 (2013)

    Article  ADS  Google Scholar 

  20. J.-L. Barrat, J.-N. Roux, J.-P. Hansen, M.L. Klein, Europhys. Lett. 7, 707 (1988)

    Article  ADS  Google Scholar 

  21. J.P. Wittmer, A. Tanguy, J.-L. Barrat, L. Lewis, Europhys. Lett. 57, 423 (2002)

    Article  ADS  Google Scholar 

  22. A. Tanguy, J.P. Wittmer, F. Leonforte, J.-L. Barrat, Phys. Rev. B 66, 174205 (2002)

    Article  ADS  Google Scholar 

  23. E. Flenner, G. Szamel, Phys. Rev. Lett. 107, 105505 (2015)

    Google Scholar 

  24. M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986)

  25. C. Klix, F. Ebert, F. Weysser, M. Fuchs, G. Maret, P. Keim, Phys. Rev. Lett. 109, 178301 (2012)

    Article  ADS  Google Scholar 

  26. H. Goldstein, J. Safko, C. Poole, Classical Mechanics, 3rd edn. (Addison-Wesley, 2001)

  27. J.F. Lutsko, J. Appl. Phys. 65, 2991 (1989)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Joachim Paul Wittmer.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wittmer, J.P., Kriuchevskyi, I., Baschnagel, J. et al. Shear-strain and shear-stress fluctuations in generalized Gaussian ensemble simulations of isotropic elastic networks. Eur. Phys. J. B 88, 242 (2015). https://doi.org/10.1140/epjb/e2015-60506-6

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2015-60506-6

Keywords

Navigation