A viscoelastic material combines recoverable elastic response with time-dependent molecular rearrangement. Its stress therefore depends not only on strain, but also on loading history and rate.

Two standard experiments reveal this behavior.

In a creep test, stress is suddenly applied and held constant. An elastic solid would jump to one strain and stay there; a viscoelastic polymer continues deforming with time.

In a stress-relaxation test, strain is suddenly imposed and held constant. The required stress decreases as chains rearrange.

Spring-and-dashpot models

A linear spring obeys $\sigma=E\varepsilon$. A dashpot idealizes viscous deformation with

$$\sigma=\eta\frac{d\varepsilon}{dt},$$

where $\eta$ is a viscosity-like material parameter.

A spring and dashpot in series form the Maxwell model. Under a suddenly imposed constant strain, its stress relaxes approximately as

$$\sigma(t)=\sigma_0 e^{-t/\tau},\qquad \tau=\frac{\eta}{E}.$$

A spring and dashpot in parallel form the Kelvin-Voigt model. Under a suddenly applied constant stress, the strain approaches its long-time value as

$$\varepsilon(t)=\frac{\sigma_0}{E}\left(1-e^{-t/\tau}\right),\qquad \tau=\frac{\eta}{E}.$$

Real polymers require combinations or distributions of relaxation times rather than one ideal element pair, but these models show why response depends on observation time.

Temperature strongly changes the rearrangement time scale. Heating usually accelerates molecular motion, so behavior observed over long times at low temperature can resemble behavior over shorter times at higher temperature.