Burgers material

Template:Short description 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

File:Burgers model 2.svg

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

$\sigma +(\frac{{\eta }_1}{E_1}+\frac{{\eta }_2}{E_2})\dot{\sigma }+\frac{{\eta }_1{\eta }_2}{E_1{E}_2}\ddot{\sigma }=({\eta }_1+{\eta }_2)\dot{\epsilon }+\frac{{\eta }_1{\eta }_2(E_1+E_2)}{E_1{E}_2}\ddot{\epsilon }$

where $\sigma$ is the stress and $\epsilon$ is the strain.

Kelvin representation

File:Burgers model.svg

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

$\sigma +(\frac{{\eta }_1}{E_1}+\frac{{\eta }_2}{E_1}+\frac{{\eta }_2}{E_2})\dot{\sigma }+\frac{{\eta }_1{\eta }_2}{E_1{E}_2}\ddot{\sigma }={\eta }_2\dot{\epsilon }+\frac{{\eta }_1{\eta }_2}{E_1}\ddot{\epsilon }$

where $\sigma$ is the stress and $\epsilon$ is the strain.

Model characteristics

File:Comparison three four element models.svg

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

External links

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