https://doi.org/10.1140/epjb/e2015-60506-6
Regular Article
Shear-strain and shear-stress fluctuations in generalized Gaussian ensemble simulations of isotropic elastic networks
1 Institut Charles Sadron, Université
de Strasbourg & CNRS, 23
rue du Loess, 67034
Strasbourg Cedex,
France
2 LCP-A2MC, Institut Jean Barriol,
Université de Lorraine & CNRS, 1 bd Arago, 57078
Metz Cedex 03,
France
a
e-mail: joachim.wittmer@ics-cnrs.unistra.fr
Received:
25
June
2015
Received in final form:
15
August
2015
Published online:
28
September
2015
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 μγγ ≡ βV ⟨ δγ̂ 2 ⟩ = (1 − λ) /Geq with β being the inverse temperature, V the volume, γ̂ the instantaneous strain and Geq the equilibrium shear modulus. Focusing on spring networks in two dimensions we show, e.g., for the stress fluctuations μττ ≡ βV ⟨ δτ̂ 2 ⟩ (τ̂ being the instantaneous stress) that μττ|λ = μA − λGeq with μA = μττ | λ = 0 being the affine shear-elasticity. For the stress autocorrelation function Cττ(t) ≡ βV⟨δτ̂(t)δτ̂(0)⟩ this result is then seen (assuming a sufficiently slow shear-stress barostat) to generalize to Cττ(t)|λ = G(t) − λGeq with G(t) = Cττ(t) | λ = 0 being the shear-stress relaxation modulus.
Key words: Solid State and Materials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2015