= Standard linear solid model
{title2=$G^*=G_L+(G_H-G_L)i\omega\tau/(1+i\omega\tau)$}
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= Standard linear solid
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A <standard linear solid model> has a finite instantaneous stiffness, a nonzero long-time stiffness and one exponential stress-relaxation mode. A <Kelvin-Voigt model> with spring $G_0$ and viscosity $\eta$ in series with spring $G_1$ gives
$$
\eta\dot\sigma+(G_0+G_1)\sigma=G_1\eta\dot\epsilon+G_0G_1\epsilon,
\qquad G_L=\frac{G_0G_1}{G_0+G_1},\quad G_H=G_1,\quad\tau=\frac\eta{G_0+G_1}.
$$
These expressions follow by adding series strains under common <stress>. Its <storage modulus> is $G_L+(G_H-G_L)x^2/(1+x^2)$ and its <loss modulus> is $(G_H-G_L)x/(1+x^2)$ for $x=\omega\tau$. Its <relaxation modulus> is $G(t)=G_L+(G_H-G_L)e^{-t/\tau}$, while its <creep compliance> is $J(t)=G_1^{-1}+G_0^{-1}(1-e^{-G_0t/\eta})$. Thus creep retardation and stress-relaxation times differ. This solid has bounded creep and cannot represent terminal fluid flow.
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