We revisit the relation between the shear-stress relaxation modulus $G\left(t\right)$, computed at finite shear strain $0<\gamma \ll 1$, and the shear-stress autocorrelation functions ${C\left(t\right)|}_{\gamma }$ and ${C\left(t\right)|}_{\tau }$ computed, respectively, at imposed strain $\gamma$ and mean stress $\tau$. Focusing on permanent isotropic spring networks it is shown theoretically and computationally that in general ${G\left(t\right)=C\left(t\right)|}_{\tau }{=C\left(t\right)|}_{\gamma }+G_{\mathrm{eq}}$ for $t>0$ with $G_{\mathrm{eq}}$ being the static equilibrium shear modulus. $G\left(t\right)$ and ${C\left(t\right)|}_{\gamma }$ thus must become different for solids and it is impossible to obtain $G_{\mathrm{eq}}$ alone from ${C\left(t\right)|}_{\gamma }$ as often assumed. We comment briefly on self-assembled transient networks where $G_{\mathrm{eq}}\left(f\right)$ must vanish for a finite scission-recombination frequency $f$. We argue that ${G\left(t\right)=C\left(t\right)|}_{\tau }{=C\left(t\right)|}_{\gamma }$ should reveal an intermediate plateau set by the shear modulus $G_{\mathrm{eq}}(f=0)$ of the quenched network.

• Received 16 May 2014
• Revised 9 December 2014

DOI:https://doi.org/10.1103/PhysRevE.91.022107