“Generalized Maxwell model”的意思、由来-开放百科全书

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Generalized Maxwell model

释义

General model form
Solids Example: standard linear solid model Liquids Example: three parameter fluid
References

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

Solids

Given elements with moduli , viscosities , and relaxation times

The general form for the model for solids is given by {{citation needed|date=November 2014}}:

{{Equation box 1 |title = General Maxwell Solid Model ({{EquationRef|1}}) |equation =

|cellpadding = 6 |border = 1 |border colour = black |background colour = white}}{{divhide|This may be more easily understood by showing the model in a slightly more expanded form:}}{{Equation box 1 |title = General Maxwell Solid Model ({{EquationRef|2}}) |equation =

|cellpadding = 6 |border = 1 |border colour = black |background colour = white}}{{divhide|end}}

Example: standard linear solid model

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

{{Equation box 1 |title = Standard Linear Solid Model ({{EquationRef|3}}) |equation =

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Liquids

Given elements with moduli , viscosities , and relaxation times

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

{{Equation box 1 |title = General Maxwell Fluid Model ({{EquationRef|4}}) |equation =

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Example: three parameter fluid

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

{{Equation box 1 |title = Three Parameter Maxwell Fluid Model ({{EquationRef|6}}) |equation =

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References

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. ^{{cite book| last = Gutierrez-Lemini| first = Danton| authorlink =| title = Engineering Viscoelasticity| publisher = Springer| series =| volume =| edition =| year = 2013| location =| pages = 88| language =| url = https://books.google.com/books?id=MbjBAAAAQBAJ&pg=PA88&lpg=PA88&dq=three+parameter+fluid+viscoelasticity| doi =| id =| isbn = 9781461481393| mr =| zbl =| jfm =}}

3 : Materials science|Non-Newtonian fluids|James Clerk Maxwell

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