Focusing on isotropic elastic networks we propose a simple-average expression $G\left(t\right)={\mu }_{\mathrm{A}}-h\left(t\right)$ for the computational determination of the shear-stress relaxation modulus $G\left(t\right)$ of a classical elastic solid or fluid. Here, ${\mu }_{\mathrm{A}}=G\left(0\right)$ characterizes the shear transformation of the system at $t=0$ and $h\left(t\right)$ the (rescaled) mean-square displacement of the instantaneous shear stress $\widehat{\tau }\left(t\right)$ as a function of time $t$. We discuss sampling time and ensemble effects and emphasize possible pitfalls of alternative expressions using the shear-stress autocorrelation function. We argue finally that our key relation may be readily adapted for more general linear response functions.

• Received 2 October 2015
• Revised 10 December 2015

DOI:https://doi.org/10.1103/PhysRevE.93.012103