Generalized Maxwell model

The Generalized Maxwell model also known as the Maxwell–Wiechert model (after James Clerk Maxwell and E Wiechert) 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 formula_1 elements with moduli formula_2, viscosities formula_3, and relaxation times formula_4
The general form for the model for solids is given by :
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formula_5
formula_6
formula_7
</math>
formula_8
formula_9
formula_10
formula_9
formula_12
formula_5
formula_6
formula_15
formula_16
formula_9
formula_18
formula_9
formula_20
Example: standard linear solid model.
Following the above model with formula_21 elements yields the standard linear solid model:
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Liquids.
Given formula_1 elements with moduli formula_2, viscosities formula_3, and relaxation times formula_4
The general form for the model for liquids is given by:
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formula_5
formula_27
</math>
formula_8
formula_9
formula_10
formula_9
formula_12
formula_5
formula_34
formula_35
formula_9
formula_37
formula_9
formula_39
Example: three parameter fluid.
The analogous model to the standard linear solid model is the three parameter fluid, also known as the Jeffreys model:
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