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

${\displaystyle \sigma +\left({\frac {\eta _{1}}{E_{1}}}+{\frac {\eta _{2}}{E_{2}}}\right){\dot {\sigma }}+{\frac {\eta _{1}\eta _{2}}{E_{1}E_{2}}}{\ddot {\sigma }}=\left(\eta _{1}+\eta _{2}\right){\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}\left(E_{1}+E_{2}\right)}{E_{1}E_{2}}}{\ddot {\varepsilon }}}$

where ${\displaystyle \sigma }$ is the stress and ${\displaystyle \varepsilon }$ is the strain.

Kelvin representation

Schematic diagram of Burgers material, Kelvin representation

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

${\displaystyle \sigma +\left({\frac {\eta _{1}}{E_{1}}}+{\frac {\eta _{2}}{E_{1}}}+{\frac {\eta _{2}}{E_{2}}}\right){\dot {\sigma }}+{\frac {\eta _{1}\eta _{2}}{E_{1}E_{2}}}{\ddot {\sigma }}=\eta _{2}{\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E_{1}}}{\ddot {\varepsilon }}}$

where ${\displaystyle \sigma }$ is the stress and ${\displaystyle \varepsilon }$ 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.

See also

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

References

1. 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