Eur. Phys. J. B (2015) 88: 242
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

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 μ_γγ ≡ βV ⟨ δγ̂ ² ⟩ = (1 − λ) /G_eq with β being the inverse temperature, V the volume, γ̂ 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 μ_ττ ≡ βV ⟨ δτ̂ ² ⟩ (τ̂ being the instantaneous stress) that μ_ττ|_λ = μ_A − λG_eq with μ_A = μ_ττ | _{λ = 0} being the affine shear-elasticity. For the stress autocorrelation function C_ττ(t) ≡ βV⟨δτ̂(t)δτ̂(0)⟩ this result is then seen (assuming a sufficiently slow shear-stress barostat) to generalize to C_ττ(t)|_λ = G(t) − λG_eq with G(t) = C_ττ(t) | _{λ = 0} being the shear-stress relaxation modulus.