$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$

Fluid supply materials may be used to simulate an external source of fluid, such as supply from microvasculature that is not modeled explicitly. The fluid supply term, $\hat{\varphi}^{w}$ , appears in the mass balance relation for the mixture, $$\divg\left(\mathbf{v}^{s}+\mathbf{w}\right)=\hat{\varphi}^{w}\,.$$ $\hat{\varphi}^{w}$ has units of reciprocal time [t$^{\mathrm{-1}}$ ]; it represents the rate at which the volume fraction of fluid changes with time.