= Viscoelasticity
{wiki}
= Viscoelastic
{synonym}
<Viscoelasticity> combines recoverable <elastic> response with dissipative and time-dependent response. Two specimens may react similarly to a rapid pull but behave differently when the same load is maintained. In a <material creep> test, constant <stress> produces evolving <strain>; in a <stress relaxation> test, fixed <strain> produces evolving <stress>.
The <Maxwell model> makes the distinction explicit by placing an <elastic> spring and viscous element in series. In simple <shear strain> it obeys
$$
\dot\gamma=\frac{\dot\tau}{G}+\frac{\tau}{\eta}.
$$
After a small step to fixed $\gamma_0$, its <shear stress> decays as $\tau(t)=G\gamma_0e^{-t/\lambda}$ with <viscoelastic relaxation time> $\lambda=\eta/G$. Under constant <shear stress> $\tau_0$, it instead continues to deform, with $\gamma(t)=\tau_0/G+\tau_0t/\eta$. These are predictions of this particular model: a <Kelvin-Voigt model> has bounded creep and different short-time behavior. <Small-amplitude oscillatory shear> measures the same competition through <storage modulus> and <loss modulus>, rather than assuming that one constant <dynamic viscosity> characterizes the material.
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