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

This material model describes a constitutive model for fibers, where a single fiber family follows an exponential power law strain energy function. The deviatoric part of the Cauchy stress is given by: $$\begin{equation} \tilde{\boldsymbol{\sigma}}=2J^{-1}H\left(\tilde{I}_{n}-1\right)\tilde{I}_{n}\frac{\partial\tilde{\Psi}}{\partial\tilde{I}_{n}}\mathbf{n}\otimes\mathbf{n}\,,\label{eq472} \end{equation}$$ and the corresponding spatial elasticity tensor is $$\begin{equation} \tilde{\boldsymbol{\mathcal{C}}}=4J^{-1}H\left(\tilde{I}_{n}-1\right)\tilde{I}_{n}^{2}\frac{\partial^{2}\tilde{\Psi}}{\partial\tilde{I}_{n}^{2}}\mathbf{n}\otimes\mathbf{n}\otimes\mathbf{n}\otimes\mathbf{n}\,,\label{eq473} \end{equation}$$ where $\tilde{I}_{n}=\tilde{\lambda}_{n}^{2}=\mathbf{N}\cdot\mathbf{\tilde{C}}\cdot\mathbf{N}$ is the square of the fiber stretch, $\mathbf{N}$ is the fiber orientation in the reference configuration, $$\begin{equation} \mathbf{N}=\sin\varphi\cos\theta\,\mathbf{e}_{1}+\sin\varphi\sin\theta\,\mathbf{e}_{2}+\cos\varphi\,\mathbf{e}_{3}\,,\label{eq474} \end{equation}$$ and $\mathbf{n}=\mathbf{\tilde{F}}\cdot\mathbf{N}/\tilde{\lambda}_{n}$ and $H\left(\cdot\right)$ is the unit step function that enforces the tension-only contribution. The fiber strain energy density is given by $$\begin{equation} \tilde{\Psi}=\frac{\xi}{\alpha\beta}\left(\exp\left[\alpha\left(\tilde{I}_{n}-1\right)^{\beta}\right]-1\right)\,,\label{eq475} \end{equation}$$ where $\xi>0$ , $\alpha\geqslant0$ and $\beta\geqslant2$ .