Burgers 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]

Model characteristics

Comparison of creep and stress relaxation for three and four element models

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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References

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

External links

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

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