Table 1.

Stress relaxation and creep formulae for the three viscoelastic models studied. The theoretical relationship between the stress relaxation and creep time constants is given in the third row {Findley, 1989 #6264}.

	Burgers Model	Generalized Maxwell Model	Standard Linear solid
Stress Relaxation	$$\sigma (t)=\frac{{\epsilon }_0}{A}\left[\left(q_1-q_2/{\tau }_{\epsilon 1}\right)e^{-t/{\tau }_{\epsilon 1}}-\left(q_1-q_2/{\tau }_{\epsilon 2}\right)e^{-t/{\tau }_{\epsilon 2}}\right]$$	$$\sigma (t)={\epsilon }_0\left[E_0^{\prime }+E_1^{\prime }{e}^{-t/{\tau }_{\epsilon 1}}+E_2^{\prime }{e}^{-t/{\tau }_{\epsilon 2}}\right]$$	$$\sigma (t)={\epsilon }_0\left[E_0^{\prime }+E_1^{\prime }{e}^{-t/{\tau }_{\epsilon 1}}\right]$$
Creep	$$\epsilon (t)={\sigma }_0\left[\frac{1}{E_1}+\frac{t}{{\eta }_1}+\frac{1}{E_2}\left(1-e^{-t/{\tau }_{\sigma }}\right)\right]$$	$$\epsilon (t)={\sigma }_0\left[\frac{1}{E_0}+\frac{1}{E_1}\left(1-e^{-t/{\tau }_{\sigma 1}}\right)+\frac{1}{E_2}\left(1-e^{-t/{\tau }_{\sigma 2}}\right)\right]$$	$$\epsilon (t)={\sigma }_0\left[\frac{1}{E_0}+\frac{1}{E_1}\left(1-e^{-t/{\tau }_{\sigma }}\right)\right]$$
Theoretical relation	$$\begin{array}{l}{\tau }_{\sigma }=\frac{q_2}{q_1}\\ {\eta }_1=q_1\end{array}$$	$$\begin{array}{l}b=\frac{E_0^{\prime }+E_1^{\prime }}{{\tau }_{\epsilon 2}}+\frac{E_0^{\prime }+E_2^{\prime }}{{\tau }_{\epsilon 1}}\\ {\tau }_{\sigma 1}=\frac{2(E_0^{\prime }+E_1^{\prime }+E_2^{\prime })}{b+\sqrt{b^2+\frac{8E_0^{\prime }(E_0^{\prime }+E_1^{\prime }+E_2^{\prime })}{{\tau }_{\epsilon 1}{\tau }_{\epsilon 2}}}}\\ {\tau }_{\sigma 2}=\frac{2(E_0^{\prime }+E_1^{\prime }+E_2^{\prime })}{b+\sqrt{b^2-\frac{8E_0^{\prime }(E_0^{\prime }+E_1^{\prime }+E_2^{\prime })}{{\tau }_{\epsilon 1}{\tau }_{\epsilon 2}}}}\end{array}$$	$${\tau }_{\sigma }={\tau }_{\epsilon }\frac{E_0+E_1}{E_0}$$