Nominal and Cauchy traction maxima under unit simple shear ($\max |T_{R}N|=\mu ,\max |Tn|=\mu (1+\sqrt{5})/2$)

For the reciprocal-Jacobian quadratic energy under $F=I+e_1\otimes e_2$, $T_R/\mu$ has off-diagonal entries $(1,2)$ and $(2,1)$ equal to one and all others zero. Every unit reference normal in the first two coordinate directions therefore maximizes nominal traction. The Cauchy stress tensor has upper-left block $\left(\begin{array}{cc}1& 1\\ 1& 0\end{array}\right)$. Its largest absolute eigenvalue is $\phi =(1+\sqrt{5})/2$, with spatial normal proportional to $(\phi ,1,0)$. Pulling this back by $F^T$ gives reference normal proportional to $(1,\phi ,0)$ and plane $x_1+\phi x_2=0$.