Burgers_material

Burgers material

Type of viscoelastic material

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.

Overview

Maxwell representation

Schematic diagram of Burgers material, Maxwell representation

Given that one Maxwell material has an elasticity $E_{1}$ and viscosity $\eta _{1}$ , and the other Maxwell material has an elasticity $E_{2}$ and viscosity $\eta _{2}$ , the Burgers model has the constitutive equation

\sigma +\left({\frac {\eta _{1}}{E_{1}}}+{\frac {\eta _{2}}{E_{2}}}\right){\dot {\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 $\sigma$ is the stress and $\varepsilon$ is the strain.

Kelvin representation

Schematic diagram of Burgers material, Kelvin representation

Given that the Kelvin material has an elasticity $E_{1}$ and viscosity $\eta _{1}$ , the spring has an elasticity $E_{2}$ and the dashpot has a viscosity $\eta _{2}$ , the Burgers model has the constitutive equation

\sigma +\left({\frac {\eta _{1}}{E_{1}}}+{\frac {\eta _{2}}{E_{1}}}+{\frac {\eta _{2}}{E_{2}}}\right){\dot {\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 $\sigma$ is the stress and $\varepsilon$ is the strain.^[1]

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This article uses material from the Wikipedia article Burgers_material, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.

[1] [1]
Malkin, Alexander Ya.; Isayev, Avraam I. (2006). Rheology: Concepts, Methods, and Applications. ChemTec Publishing. pp. 59–60. ISBN 9781895198331.

[1]

Burgers_material

Burgers material

Overview

Maxwell representation

Kelvin representation

Model characteristics

See also

References

External links

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