$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\Grad}{\operatorname{Grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$ $\newcommand{\Divg}{\operatorname{Div}}$ $\newcommand{\cay}{\operatorname{cay}}$ $\newcommand{\rot}{\operatorname{rot}}$

For this model, the active stress is acting along a prescribed direction given by the unit vector $\mathbf{a}_{r}$ in the reference configuration. The $2^{\text{nd}}$ Piola-Kirchhoff stress is $$\begin{equation} \mathbf{S}^{a}=T^{a}\mathbf{a}_{r}\otimes\mathbf{a}_{r}\,,\label{eq519} \end{equation}$$ and the Cauchy stress is $$\begin{equation} \boldsymbol{\sigma}^{a}=J^{-1}T^{a}\mathbf{a}\otimes\mathbf{a}\,,\label{eq520} \end{equation}$$ where $T^{a}$ is the prescribed contractile stress and $\mathbf{a}=\mathbf{F}\cdot\mathbf{a}_{r}$ . Since $\mathbf{S}^{a}$ is not a function of deformation, the material and spatial tangents are both zero.