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

Consider a porous medium with an interstitial fluid that consists of a solvent and one or more solutes, whose boundary is permeable to the solvent but not to the solutes (e.g., a biological cell). Since solutes are trapped within such a medium, $c_{r}$ is a constant in this type of problem. Since the boundary is permeable to the solvent, $\tilde{p}$ must be continuous across the boundary. Assuming ideal physicochemical conditions, $\Phi=1$ , and zero ambient pressure, this continuity requirement implies that $p=R\theta\left(c-c^{\ast}\right)$ , where $c^{\ast}$ is the osmolarity of the external environment. Using (2.9-2), it follows that $$\begin{equation} p=R\theta\left(\frac{c_{r}}{J-\varphi_{r}^{s}}-c^{\ast}\right)\,.\label{eq144} \end{equation}$$ The reference configuration (the stress-free configuration of the solid) is achieved when $J=1$ and $p=0$ , from which it follows that $c_{r}=\left(1-\varphi_{r}^{s}\right)c_{0}^{\ast}$ , where $c_{0}^{\ast}$ is the value of $c^{\ast}$ in the reference state. Therefore (2.9.1-1) may also be written as $$\begin{equation} p=R\theta c^{\ast}\left(\frac{1-\varphi_{r}^{s}}{J-\varphi_{r}^{s}}\frac{c_{0}^{\ast}}{c^{\ast}}-1\right)\,,\label{eq145} \end{equation}$$ and this expression may be substituted into (2.9-3) to evaluate the corresponding elasticity tensor.