Burgers material

 ( Non-newtonian Fluids ) 

A Burgers material is a viscoelastic material having the properties both of elasticity and viscosity. It is named after the Dutch physicist Johannes Martinus Burgers.

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Overview

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Maxwell representation Given that one Maxwell material has an elasticity $E\_1$ and viscosity $\backslash eta\_1$, and the other Maxwell material has an elasticity $E\_2$ and viscosity $\backslash eta\_2$, the Burgers model has the constitutive equation

$\backslash sigma\; +\; \backslash left(\; \backslash frac\; \{\backslash eta\_1\}\; \{E\_1\}\; +\; \backslash frac\; \{\backslash eta\_2\}\; \{E\_2\}\; \backslash right)\; \backslash dot\backslash sigma\; +$

\frac {\eta_1 \eta_2} {E_1 E_2} \ddot\sigma = \left( \eta_1 + \eta_2 \right) \dot\varepsilon + \frac {\eta_1 \eta_2 \left( E_1 + E_2 \right)} {E_1 E_2} \ddot\varepsilon where $\backslash sigma$ is the stress and $\backslash varepsilon$ is the strain.

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Kelvin representation Given that the Kelvin material has an elasticity $E\_1$ and viscosity $\backslash eta\_1$, the spring has an elasticity $E\_2$ and the dashpot has a viscosity $\backslash eta\_2$, the Burgers model has the constitutive equation

$\backslash sigma\; +\; \backslash left(\; \backslash frac\; \{\backslash eta\_1\}\; \{E\_1\}\; +\; \backslash frac\; \{\backslash eta\_2\}\; \{E\_1\}\; +\; \backslash frac\; \{\backslash eta\_2\}\; \{E\_2\}\; \backslash right)\; \backslash dot\backslash sigma\; +$

\frac {\eta_1 \eta_2} {E_1 E_2} \ddot\sigma = \eta_2\dot\varepsilon + \frac {\eta_1 \eta_2} {E_1} \ddot\varepsilon where $\backslash sigma$ is the stress and $\backslash varepsilon$ is the strain.

(2025). 9781895198331, ChemTec Publishing. ISBN 9781895198331

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Model characteristics This model incorporates viscous flow into the standard linear solid model, giving a linearly increasing asymptote for strain under fixed loading conditions.

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See also

• Generalized Maxwell model
• Kelvin–Voigt material
• Maxwell material
• Standard linear solid model

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External links

• Creep and Stress Relaxation for Four-Element Viscoelastic Solids and Liquids, Wolfram Demonstrations Project

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