 Johnson-Segalman steady viscometric functions

For stress $-pI+\alpha G_{0}A+2{\mu }_{0}E$ and slip derivative $D_{t}A+\Omega A-A\Omega -\alpha (EA+AE)=-(A-I)/\tau$, the steady viscometric functions are $\mu ={\mu }_0+{\alpha }^2{G}_0\tau /D$, ${\psi }_1=2{\alpha }^2{G}_0{\tau }^2/D$ and ${\psi }_2=-(1-\alpha ){\psi }_1/2$. Solving the three symmetric xy conformation equations gives $A_{xy}=\alpha \tau \dot{\gamma }/D$, $A_{xx}=1+(1+\alpha )\tau \dot{\gamma }{A}_{xy}$, $A_{yy}=1-(1-\alpha )\tau \dot{\gamma }{A}_{xy}$ and $A_{zz}=1$.