momentum should be solved to determine the local state of strain and stress.

The deformation of the tissue is characterised by the map $\Bvarphi(\bX,t)$. Recognising that, in tendons, the solid collagen fibrils and fibroblasts do not undergo mass transport, the material velocity of this species, $\bV =
\partial\Bvarphi/\partial t$, is used as the primitive variable for mechanics. Each remaining species can undergo mass transport relative to the solid collagen. For this purpose, it is useful to define the material velocity of a species $\iota$ *relative to the solid skeleton* as: $\bV^\iota =
(1/\rho_0^\iota)\bF\bM^\iota$. Thus, the total material velocity of a species $\iota$ is $\bV+\bV^\iota$.

The total first Piola-Kirchhoff stress tensor, $\bP$, is the sum of the partial stresses $\bP^{\,\iota}$ (borne by a species $\iota$) over all the species present. Recognizing that solutes in low concentrations, and do not bear appreciable stress, the partial stresses and momentum balance equation are defined only for the solid collagen and fluid phases. With the introduction of these quantities, the balance of linear momentum in local form over $\Omega_0$ for solid collagen and fluid is,

$$\begin{split}
\rho_0^\iota\frac{\partial}{\partial t}\left(\bV+\bV^\iota\right) &
=\rho^\iota_0\left(\bg+\bq^\iota\right) +
\mathrm{\small{DIV}}[\bP^{\,\iota}]\\ 
& \quad -\left(\mathrm{\small{GRAD}}\left[\bV+
  \bV^\iota\right]\right)\bM^\iota, \quad \iota = \mathrm{c,f}
\label{linearmombalance}
\end{split}$$

where $\bg$ is 