Lower-convected stress pull-back
= Lower-convected stress pull-back
{title2=$\dot{(F^T\tau F)}=F^T(\dot\tau+L^T\tau+\tau L)F$}
For $L=\dot FF^{-1}$, the product rule proves the displayed <lower-convected derivative> identity. Under a superposed rotation $Q(t)$, $\tau^*=Q\tau Q^T$ and $L^*=QLQ^T+\dot QQ^T$. The two rotation terms in $\dot\tau^*$ cancel those in $(L^*)^T\tau^*+\tau^*L^*$, proving that the lower-convected rate is an <objective time derivative>.