Renovating shear flow ($S(a)=\left(\begin{array}{cc}1& a\\ 0& 1\end{array}\right),a=\Lambda T$)

A renovating shear flow holds a planar shear flow fixed for an interval $T$, then chooses a fresh orientation independently of preceding intervals. Each interval acts on a material line by a rotated copy of the displayed deformation gradient. The orientation law must be specified: independent uniformly distributed orientations define the isotropic model, whereas a biased orientation law generally gives another Lyapunov exponent.