which we elaborate below, and that $\bF^{\mathrm{e}^\mathrm{f}}\bF^{\mathrm{g}^\mathrm{f}} =
\bF$. As with the solid collagen we admit $\bF^{\mathrm{e}^\mathrm{f}}
=
\overline{\bF}^{\mathrm{e}^\mathrm{f}}\widetilde{\bF}^{\mathrm{e}^\mathrm{f}}$, the sub-components carrying the same interpretation as for the solid collagen. However, we do not explicitly use this last decomposition.

The elastic-growth decomposition is visualised in . Assuming that the volume changes associated with growth described above are isotropic, a simple form for the growth part of the deformation gradient tensor is

$$\bF^{\mathrm{g}^\iota} = \left(
  \frac{\rho_0^\iota}{\rho_{0_{\mathrm{ini}}}^\iota} \right)^
  {\frac{1}{3}} 
{\bf 1},\quad \iota = \mathrm{c,f}
\label{isotropicgrowth}$$

where $\rho_{0_{\mathrm{ini}}}^\iota(\bX)$ is the reference concentration at the initial time, and [**1**]{} is the second-order isotropic tensor.[^7] In the state, $\bF = \bF^{\mathrm{g}^\iota}$, the species would be stress free. The kinematics being local, the action of $\bF^{\mathrm{g}^\iota}$ alone can result in incompatibility, which is eliminated by the geometrically-necessary elastic deformation $\widetilde{\bF}^{\mathrm{e}^{\mathrm{\iota}}}$, which causes an internal, self-equilibrated stress. The component $\overline{\bF}^{\mathrm{e}^\iota}$ is associated with the external stress.

### Saturation and tissue swelling {#satswel}

The degree of saturation of the solid phase plays a fundamental role in determining whether the tissue responds to an infusion (expulsion) of fluid by swelling (shrinking). In particular, the isotropic swelling law defined by Equation (\[isotropicgrowth\]) has to be generalised to treat the case 