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

Biphasic materials may be used to model a porous medium consisting of a mixture of a porous-permeable solid matrix and an interstitial fluid. Each of these mixture constituents is assumed to be intrinsically incompressible. This means that the true densities of the solid and fluid are invariant in space and time; this assumption further implies that a biphasic mixture will undergo zero volume change when subjected to a hydrostatic fluid pressure. Yet the mixture is compressible because the pores of the solid matrix may gain or lose fluid under general loading conditions. The Cauchy stress ${\rm \boldsymbol{\sigma}}$ in a biphasic material is given by $$\begin{equation} \boldsymbol{\sigma}=-p\mathbf{I}+{\rm \boldsymbol{\sigma}}^{e}\,,\label{eq:bp-stress} \end{equation}$$ where $p$ is the interstitial fluid pressure and $\boldsymbol{\sigma}^{e}$ is the stress resulting from the deformation of the porous solid matrix. Therefore, the constitutive relation of the solid matrix should be chosen from the list of unconstrained materials provided in Section 4.1.3↑. The user is referred to the FEBio Theory Manual for a general description of the biphasic theory.