Simple-average expressions for shear-stress relaxation modulus

TL;DR

The paper introduces a simple-average formula for calculating the shear-stress relaxation modulus in elastic networks, linking it to shear stress fluctuations and autocorrelation functions, with potential broader applications.

Contribution

It proposes a novel simple-average expression for shear-stress relaxation modulus, connecting it to stress fluctuations and autocorrelation functions, applicable to elastic solids and fluids.

Findings

The new expression accurately computes G(t) from stress data.

Sampling time effects on the measurement are analyzed.

The approach can be adapted for other linear response functions.

Abstract

Focusing on isotropic elastic networks we propose a novel simple-average expression $G(t) = \mu_A - h(t)$ for the computational determination of the shear-stress relaxation modulus $G(t)$ of a classical elastic solid or fluid and its equilibrium modulus $\G_{eq} = \lim_{t \to \infty} G(t)$. Here, $\mu_A = G(0)$ characterizes the shear transformation of the system at $t=0$ and $h(t)$ the (rescaled) mean-square displacement of the instantaneous shear stress $\hat{\tau}(t)$ as a function of time $t$. While investigating sampling time effects we also discuss the related expressions in terms of shear-stress autocorrelation functions. We argue finally that our key relation may be readily adapted for more general linear response functions.