Burgers material
= Burgers material
{c}
{title2=$J(t)=1/E_0+(1/E_1)(1-e^{-t/\tau})+t/\eta_0$}
{wiki}
= Burgers model
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{synonym}
A four-element <linear viscoelasticity> model with a <spring> $E_0$, a <Kelvin-Voigt model> branch $E_1,\eta_1$, and a free <dashpot> $\eta_0$ in series. Adding their <strains> under common <stress> gives the displayed <creep compliance>, with $\tau=\eta_1/E_1$. There is an instantaneous elastic response, a delayed recoverable response and steady viscous flow.https://docs.itascasoftware.com/pfc600/common/models/burgers/doc/modelburgers.html[Burgers Model, PFC 6.0 documentation, Figure 1 and equations (1)–(2), (5): Kelvin and Maxwell units in series]{ref} Named after <Johannes Martinus Burgers>, it extends a <Maxwell model> with a delayed elastic branch, or a <standard linear solid model> with a free dashpot.
For a load $\sigma_0$ maintained for time $t_h$, the two recoverable contributions behave as in <recovery after a finite-duration stress load>, while the free <dashpot> retains $\sigma_0t_h/\eta_0$. Hence
$$
\varepsilon(t)=\frac{\sigma_0}{E_1}(1-e^{-t_h/\tau})e^{-(t-t_h)/\tau}
+\frac{\sigma_0t_h}{\eta_0},\qquad t>t_h,
\qquad\boxed{\varepsilon(\infty)=\frac{\sigma_0t_h}{\eta_0}}.
$$
This residual response models viscous flow; it does not by itself establish a plastic yield threshold or a damage mechanism in a real specimen.
\Image[/rheology-creep-recovery.png]
{title=Immediate recovery, delayed recovery and residual viscous strain}
{description=Original predictions for a standard linear solid and a Burgers material under the same finite-duration load. Dimensionless illustrative parameters; no experimental rubber or wood data are fitted.}