 Solution

For a rubber-like solid, a spring is a first model of recoverable elasticity, while a viscous element can represent rate-dependent loss and delayed recovery. An immediate extension followed by bounded delayed material creep is represented by series spring and Voigt-branch creep, a standard linear solid model:The first term is immediate and recoverable; the second is delayed and also recoverable. For a load held until $t=t_h$, recovery after a finite-duration stress load predicts an immediate drop of ${\sigma }_0/E_0$ on unloading, followed byThis supplies a direct comparison with a loading-and-unloading observation: the model returns completely to its original length, with separate immediate and delayed recovery. A single Kelvin-Voigt model misses the immediate compliance, while a free series dashpot would predict unbounded flow that an intact crosslinked rubber need not show. A spring alone suffices over a timescale on which the measured response is effectively immediate and elastic.

These are local small-strain analogues. Large-strain rubber elasticity is nonlinear, nearly incompressible and sensitive to temperature, loading history and internal damage. A small set of linear springs and dashpots cannot reproduce every amplitude, timescale or hysteresis loop.

No numerical rubber trace or fitted constants are supplied, so these are explicit qualitative model predictions for comparison with the practical observations.