Numerical determination of shear stress relaxation modulus of polymer glasses

Focusing on simulated polymer glasses well below the glass transition, we confirm the validity and the efficiency of the recently proposed simple-average expression $G(t) = \mu_A - h(t)$ for the computational determination of the shear stress relaxation modulus $G(t)$. Here, $\mu_A = G(0)$ characterizes the affine shear transformation of the system at $t=0$ and $h(t)$ the mean-square displacement of the instantaneous shear stress as a function of time $t$. This relation is seen to be particulary useful for systems with quenched or sluggish transient shear stresses which necessarily arise below the glass transition. The commonly accepted relation $G(t)=c(t)$ using the shear stress auto-correlation function $c(t)$ becomes incorrect in this limit.