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.

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.

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]

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

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

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