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.

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.