Generalized Maxwell model

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Schematic of Maxwell–Wiechert model

The Generalized Maxwell model also known as the Maxwell–Wiechert model (after James Clerk Maxwell and E Wiechert[1][2]) 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.[3][4]

General model form[edit]


Given elements with moduli , viscosities , and relaxation times

The general form for the model for solids is given by[citation needed]:

General Maxwell Solid Model (1)

Example: standard linear solid model[edit]

Following the above model with elements yields the standard linear solid model:

Standard Linear Solid Model (3)


Given elements with moduli , viscosities , and relaxation times

The general form for the model for liquids is given by:

General Maxwell Fluid Model (4)

Example: three parameter fluid[edit]

The analogous model to the standard linear solid model is the three parameter fluid, also known as the Jeffrey model:[5]

Three Parameter Maxwell Fluid Model (6)


  1. ^ Wiechert, E (1889); "Ueber elastische Nachwirkung", Dissertation, Königsberg University, Germany
  2. ^ Wiechert, E (1893); "Gesetze der elastischen Nachwirkung für constante Temperatur", Annalen der Physik, 286, 335–348, 546–570
  3. ^ Roylance, David (2001); "Engineering Viscoelasticity", 14-15
  4. ^ Tschoegl, Nicholas W. (1989); "The Phenomenological Theory of Linear Viscoelastic Behavior", 119-126
  5. ^ Gutierrez-Lemini, Danton (2013). Engineering Viscoelasticity. Springer. p. 88. ISBN 9781461481393.