Steady simple shear of an Oldroyd-A fluid
= Steady simple shear of an Oldroyd-A fluid
{title2=$N_1=2(\mu-\mu_r)\tau\dot\gamma^2$}
For constant <simple shear flow> rate $s$, the nonpressure stress in the component-first gradient convention $L_{12}=s$ is
$$
\sigma^d=\begin{pmatrix}0&\mu s&0\\\mu s&-2(\mu-\mu_r)\tau s^2&0\\0&0&0\end{pmatrix}.
$$
Thus the first <normal-stress difference> is $N_1=2(\mu-\mu_r)\tau s^2$, while the second is $N_2=-N_1$. Adding the incompressibility <pressure> changes neither difference.