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

Abstract

Shear-strain and shear-stress correlations in isotropic elastic bodies are investigated both theoretically and numerically at either imposed mean shear-stress $\tau$ ($\lambda =0$) or shear-strain $\gamma$ ($\lambda =1$) and for more general values of a dimensionless parameter $\lambda$ characterizing the generalized Gaussian ensemble. It allows to tune the strain fluctuations $μ_{γγ} \equiv βV \la δγ^2 \ra = (1-λ)/G_{eq}$ with $\beta$ being the inverse temperature, $V$ the volume, $\gamma$ 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 $μ_{ττ} \equiv βV \la δτ^2 \ra$ ($\tau$ being the instantaneous stress) that ${\mu }_{\tau \tau }={\mu }_A-\lambda G_{eq}$ with ${\mu }_A={\mu }_{\tau \tau }{|}_{\lambda =0}$ being the affine shear-elasticity. For the stress autocorrelation function $c_{ττ}(t) \equiv βV \la δτ(t) δτ(0) \ra$ this result is then seen (assuming a sufficiently slow shear-stress barostat) to generalize to $c_{ττ}(t) = G(t) - λ\Geq$ with $G(t)$ being the shear-stress relaxation modulus.

17 pages, 15 figures

References in corpus (3)

• Generalized canonical ensembles and ensemble equivalence
• Shear stress relaxation and ensemble transformation of shear stress autocorrelation functions revisited
• Compressibility and pressure correlations in isotropic solids and fluids

Cited by in corpus (6)

• Shear modulus and shear-stress fluctuations in polymer glasses
• Shear-stress fluctuations in self-assembled transient elastic networks
• Shear-stress fluctuations and relaxation in polymer glasses
• Simple-average expressions for shear-stress relaxation modulus
• Structural features and nonlinear rheology of self-assembled networks of cross-linked semiflexible polymers
• Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosity