Generalized Maxwell model
The Generalized Maxwell model also known as the Maxwell–Wiechert model is the most general form of the linear model for viscoelasticity. In this model several Maxwell elements are assembled in parallel. It takes into account that the relaxation does not occur at a single time, but in a set of times. Due to the presence of molecular segments of different lengths, with shorter ones contributing less than longer ones, there is a varying time distribution. The Wiechert model shows this by having as many spring–dashpot Maxwell elements as are necessary to accurately represent the distribution. The figure on the right shows the generalised Wiechert model.General model form
Solids
Given elements with moduli, viscosities, and relaxation times
The general form for the model for solids is given by :Following the above model with elements yields the standard linear solid model:Liquids
Given elements with moduli, viscosities, and relaxation times
The general form for the model for liquids is given by:Example: three parameter fluid
The analogous model to the standard linear solid model is the three parameter fluid, also known as the Jeffreys model:
