Mechanical models are often used to describe the viscoelastic behavior of polymers. The Maxwell model, which consists of a spring and dashpot in series, predicts that the variation of strain, e, with time, t, for a viscoelastic material can be described by an equation of the form

de 1 do dt E dt + | 9E= modulus of spring, \eta = viscosity of dashpot, where \sigma is the applied stress. The Voigt model, which consists of a spring and dashpot in parallel, leads to an equation of the form

\frac{de}{dt} = \frac{\sigma }{\eta } - \frac{Ee}{\eta }

(a) Derive equations describing the variation of strain with time for both models subjected to a constant stressing-rate (i. e. \frac{d\sigma }{dt } = constant).

(b) Derive equations describing the variation of stress with time when both models are subjected to a constant strain-rate (i. e. \frac{de}{dt} = constant).