Fluctuation-dissipation relation between shear stress relaxation modulus and shear stress autocorrelation function revisited

Abstract

The shear stress relaxation modulus G(t) may be determined from the shear stress after switching on a tiny step strain γ or by inverse Fourier transformation of the storage modulus G′(ω) or the loss modulus G″(ω) obtained in a standard oscillatory shear experiment at angular frequency ω. It is widely assumed that G(t) is equivalent in general to the equilibrium stress autocorrelation function which may be readily computed in computer simulations (β being the inverse temperature and V the volume). Focusing on isotropic solids formed by permanent spring networks we show theoretically by means of the fluctuation-dissipation theorem and computationally by molecular dynamics simulation that in general G(t) = Geq + C(t) for t > 0 with Geq being the static equilibrium shear modulus. A similar relation holds for G′(ω). G(t) and C(t) must thus become different for a solid body and it is impossible to obtain Geq directly from C(t).