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 A − λ 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.
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References
M. Allen, D. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1994)
J.L. Lebowitz, J.K. Percus, L. Verlet, Phys. Rev. 153, 250 (1967)
H.B. Callen, Thermodynamics and an Introduction to Thermostatistics (Wiley, New York, 1985)
D. Frenkel, B. Smit, Understanding Molecular Simulation – From Algorithms to Applications, 2nd edn. (Academic Press, San Diego, 2002)
D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2000)
J. Thijssen, Computational Physics (Cambridge University Press, Cambridge, 1999)
M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1954)
J.P. Wittmer, H. Xu, P. Polińska, F. Weysser, J. Baschnagel, J. Chem. Phys. 138, 12A533 (2013)
J.P. Wittmer, H. Xu, J. Baschnagel, Phys. Rev. E 91, 022107 (2015)
J.P. Wittmer, H. Xu, O. Benzerara, J. Baschnagel, Mol. Phys. (2015), DOI: 10.1080/0268976.2015.1023225
J. Hansen, I. McDonald, Theory of Simple Liquids, 3rd edn. (Academic Press, New York, 2006)
J. Hetherington, J. Low Temp. Phys. 66, 145 (1987)
M. Costeniuc, R. Ellis, H. Touchette, B. Turkington, Phys. Rev. E 73, 026105 (2006)
K. van Workum, J. de Pablo, Phys. Rev. E 67, 011505 (2003)
T. Witten, P.A. Pincus, Structured Fluids: Polymers, Colloids, Surfactants (Oxford University Press, Oxford, 2004)
M. Rubinstein, R. Colby, Polymer Physics (Oxford University Press, Oxford, 2003)
J.P. Wittmer, H. Xu, P. Polińska, C. Gillig, J. Helfferich, F. Weysser, J. Baschnagel, Eur. Phys. J. E 36, 131 (2013)
D.R. Squire, A.C. Holt, W.G. Hoover, Physica 42, 388 (1969)
H. Mizuno, S. Mossa, J.-L. Barrat, Phys. Rev. E 87, 042306 (2013)
J.-L. Barrat, J.-N. Roux, J.-P. Hansen, M.L. Klein, Europhys. Lett. 7, 707 (1988)
J.P. Wittmer, A. Tanguy, J.-L. Barrat, L. Lewis, Europhys. Lett. 57, 423 (2002)
A. Tanguy, J.P. Wittmer, F. Leonforte, J.-L. Barrat, Phys. Rev. B 66, 174205 (2002)
E. Flenner, G. Szamel, Phys. Rev. Lett. 107, 105505 (2015)
M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986)
C. Klix, F. Ebert, F. Weysser, M. Fuchs, G. Maret, P. Keim, Phys. Rev. Lett. 109, 178301 (2012)
H. Goldstein, J. Safko, C. Poole, Classical Mechanics, 3rd edn. (Addison-Wesley, 2001)
J.F. Lutsko, J. Appl. Phys. 65, 2991 (1989)
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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
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DOI: https://doi.org/10.1140/epjb/e2015-60506-6