= Solution
A <Kelvin-Voigt model> has no finite instantaneous elastic compliance: the viscous element prevents a sudden deformation under a finite <stress> step. Its <creep compliance> is
$$
J_K(t)=\frac1{G_0}\left(1-e^{-G_0t/\eta_0}\right),\qquad J_K(0^+)=0.
$$
Conversely an ideal <strain> step requires an impulsive <stress>,
$$
\sigma(t)=\epsilon_0[G_0H(t)+\eta_0\delta(t)].
$$
After the impulse the held-strain response is simply constant. There is no finite stress-decay interval, and the <loss modulus> grows without bound as $\omega\to\infty$. This fails to represent a material with both a finite instantaneous stiffness and delayed <stress relaxation>.
The added series spring resolves this particular defect. At the instant of loading the Kelvin element cannot move but the added spring can. The <standard linear solid model> consequently has
$$
\boxed{G(t)=G_L+(G_H-G_L)e^{-t/\tau},\qquad t\geq0,}
$$
and
$$
\boxed{J(t)=\frac1{G_1}+\frac1{G_0}\left(1-e^{-G_0t/\eta_0}\right).}
$$
Its instantaneous stiffness is $G_H=G_1$, its long-time stiffness is $G_L$, and it exhibits genuine <stress relaxation> as well as delayed creep. The creep retardation time $\eta_0/G_0$ differs from the stress-relaxation time $\tau=\eta_0/(G_0+G_1)$. These properties also follow directly from its constitutive equation,
$$
\eta_0\dot\sigma+(G_0+G_1)\sigma=G_1\eta_0\dot\epsilon+G_0G_1\epsilon.
$$
It remains an idealized solid with one relaxation mode: it cannot describe unrestricted long-time viscous flow, nonlinear response, or a broad spectrum of relaxation times.
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