Burgers material

Example

The Burgers material is a Maxwell material with spring modulus $E_1 > 0$ and dashpot viscosity $\eta_1 > 0$. It is in series with a Kelvin–Voigt material with spring modulus $E_2 > 0$ and dashpot viscosity $\eta_2 > 0$. In series the stress is common and the strains add. Creep: under a stress step $\sigma_0$ at time $0$, the Maxwell part contributes $\sigma_0/E_1 + \sigma_0 t/\eta_1$ and the Kelvin–Voigt part contributes $(\sigma_0/E_2)(1 - e^{-E_2 t/\eta_2})$, so $$\varepsilon(t) = \frac{\sigma_0}{E_1} + \frac{\sigma_0 t}{\eta_1} + \frac{\sigma_0}{E_2} \left(1 - e^{-E_2 t / \eta_2}\right).$$ This creep curve has an instantaneous jump, a primary stage with decreasing rate, and a secondary stage with constant rate $\sigma_0/\eta_1$.