Retardation time (viscoelasticity, ${\tau }_r$)

The characteristic time for a delayed strain response to approach equilibrium under a step in stress. For a Kelvin-Voigt model with elastic modulus $E$ and viscosity $\eta$, the equation $\eta \dot{\epsilon }+E\epsilon ={\sigma }_0$ gives $\epsilon =({\sigma }_0/E)(1-e^{-t/{\tau }_r})$, where ${\tau }_r=\eta /E$. A relaxation time instead describes decay of stress after an imposed strain; the two times need not coincide in a standard linear solid model.