Series spring and Voigt-branch creep ($J(t)=1/E_0+(1/E_1)(1-e^{-E_{1}t/\eta })$)

A spring $E_0$ in series with a parallel spring-dashpot branch $E_1,\eta$ has creep compliance $J(t)=1/E_0+(1/E_1)(1-e^{-E_{1}t/\eta })$. It includes immediate and delayed recoverable strain, but no unbounded viscous flow. Large strain, damage or anisotropy require additional constitutive structure.

Apply constant stress ${\sigma }_0$ at $t=0$ and remove it at $t=t_h$. For series spring and Voigt-branch creep, the series spring recovers its strain ${\sigma }_0/E_0$ immediately on unloading. The Kelvin-Voigt model branch has retardation time $\tau =\eta /E_1$ and must keep continuous strain because an instantaneous dashpot displacement would require an impulse. Its post-unloading equation is $\eta \dot{\epsilon }+E_1\epsilon =0$. Solving with the branch's strain at $t_h$ gives the title formula. Thus all remaining strain eventually recovers: this standard linear solid model has no permanent set.