+
\frac{\gamma}{\beta}({J^{\mathrm{e}^{\mathrm{c}^{-2\beta}}}} -1) +
\gamma{\bf 1}\colon(\bC^{\mathrm{e}^{\mathrm{c}}}-{\bf 1})\\ &-\frac{N
k \theta}{4\sqrt{2L/A}}\left(\sqrt{\frac{2A}{L}} + \frac{1}{4(1 -
\sqrt{2A/L})} -\frac{1}{4} \right) Z,\\ Z &=
\log\left(\lambda_1^{{\mathrm{e}}^{a^\mathrm{2}}}
\lambda_2^{{\mathrm{e}}^{b^\mathrm{2}}}
\lambda_3^{{\mathrm{e}}^{c^\mathrm{2}}}\right).
\label{wlcmeq}
\end{split}$$

Here, $N$ is the density of chains, and $a,b$ and $c$ are lengths of the unit cell sides aligned with the principal stretch directions. The material model is isotropic only if $a=b=c$.

The elastic stretches along the unit cell axes are, respectively, denoted by $\lambda_1^{\mathrm{e}},
\lambda_2^{\mathrm{e}}$ and $\lambda_3^{\mathrm{e}}$, $\bC^{\mathrm{e}^{\mathrm{c}}} =
\bF^{\mathrm{e}^{\mathrm{c}^{\mathrm{T}}}}
\bF^{\mathrm{e}^{\mathrm{c}}}$ is the elastic right Cauchy-Green tensor of collagen. The factors $\gamma$ and $\beta$ control the bulk compressibility of the model. The end to end chain length is given by $r = \frac{1}{2}\sqrt{a^2\lambda_1^{\mathrm{e}^2} +
  b^2\lambda_2^{\mathrm{e}^2}+c^2\lambda_3^{\mathrm{e}^2}}$, where $\lambda^\mathrm{e}_I = 
\sqrt{\bN_I\cdot\bC^{\mathrm{e}^{\mathrm{c}}}\bN_I}$, and $\bN_I,\,I =
1,2,3$ are the unit vectors along the three unit cell axes, respectively. In our numerical simulations that appear below in Section \[numericalimplementation\], the numerical values used for the parameters introduced in (\[wlcmeq\]) are based on those in @kuhlremod05.

A nearly incompressible ideal fluid {#compfluid}
-----------------------------------

In this preliminary work, the fluid phase is treated as nearly incompressible and ideal, i.e., inviscid. The partial Cauchy stress in the fluid is $$\Bsigma^\mathrm{f} =
\mathrm{det}(\bF^{\mathrm{e}^\mathrm{f}})^{-1}
\bP^{\,\mathrm{f}}\bF^{\mathrm{e}^\mathrm{fT}} 
= h(\rho^\mathrm{f}){\bf 1},\label{Pf}$$

where a large value of $h^\prime(\rho^\mathrm{f})$ ensures 