Mathematical Models of Viscoelastic Behaviour

Over the years there have been many attempts to simulate the behaviour of viscoelastic materials. This has been aimed at (i) facilitating analysis of the behaviour of plastic products, (ii) assisting with extrapolation and interpolation of experimental data and (iii) reducing the need for extensive, time-consuming creep tests. The most successful of the mathematical models have been based on spring and dashpot elements to represent, respectively, the elastic and viscous responses of plastic materials. Although there are no discrete molecular structures which behave like the individual elements of the models, nevertheless 

The Maxwell Model consists of a spring and dashpot in series at shown in Fig. 2.34. This model may be analysed as follows. 

The spring is the elastic component of the response and obeys the relation 

The dashpot is the viscous component of the response and in this case the stress (72 is proportional to the rate of strain f2 ie 

For equilibrium of forces, assuming constant area Applied Stress, a = u = ctj 

---