Burgers material
# 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

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

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.

## Model characteristics

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

