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

A time varying “elastance” active contraction model [35] was added to the transversely isotropic materials. When active contraction is activated, the total Cauchy stress $\mathbf{\sigma}$ is defined as the sum of the active stress tensor $\boldsymbol{\sigma}^{a}=T^{a}\mathbf{a}\otimes\mathbf{a}$ and the passive stress tensor $\boldsymbol{\sigma}^{p}$ : $$\begin{equation} \boldsymbol{\sigma}=\boldsymbol{\sigma}^{p}+\boldsymbol{\sigma}^{a},\label{eq516} \end{equation}$$ where a is the deformed fiber vector (unit length), defined as $\lambda\mathbf{a}=\mathbf{F}\cdot\mathbf{a}$ . The time varying elastance model is a modification of the standard Hill equation that scales the standard equation by an activation curve $C\left(t\right)$ . The active fiber stress $T^{a}$ is defined as: $$\begin{equation} T^{a}=T_{\max}\frac{Ca_{0}^{2}}{Ca_{0}^{2}+ECa_{50}^{2}}C\left(t\right),\label{eq517} \end{equation}$$ where $T_{max}=135.7\,\text{kPa}$ is the isometric tension under maximal activation at the peak intracellular calcium concentration of $\text{Ca}_{0}=4.35\,\mu\text{M}$ . The length dependent calcium sensitivity is governed by the following equation: $$\begin{equation} ECa_{50}=\frac{\left(\text{Ca}_{0}\right)_{\max}}{\sqrt{\exp\left[B(l-l_{0})\right]-1}}\,,\label{eq518} \end{equation}$$ where $\left(\text{Ca}_{0}\right)_{\max}=4.35\,\mu\text{M}$ is the maximum peak intracellular calcium concentration, $B=4.75\,\mu\text{m}^{-1}$ governs the shape of the peak isometric tension-sarcomere length relation, $l_{0}=1.58\,\mu\text{m}$ is the sarcomere length at which no active tension develops, and $l$ is the sarcomere length which is the product of the fiber stretch $\lambda$ and the sarcomere unloaded length $l_{r}=2.04\,\mu\text{m}$ .