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Subsection 4.7.1: General Specification of Multigeneration Solids Up Chapter 4: Materials Subsection 4.8.1: General Specification of Biphasic Materials

## 4.8 Biphasic Materials

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 in a biphasic material is given by where is the interstitial fluid pressure and 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.
In addition to selecting a constitutive relation for the solid matrix, a constitutive relation must also be selected for the hydraulic permeability of the interstitial fluid flowing within the porous deformable solid matrix. The hydraulic permeability relates the volumetric flux of the fluid relative to the solid, , to the interstitial fluid pressure gradient, , according to where is the hydraulic permeability tensor. (Note that this expression does not account for the contribution of external body forces on the fluid.)
The governing equations for biphasic materials are the mixture momentum balance under quasi-static conditions, in the absence of external body force, and the mixture mass balance, where is the solid velocity.

Subsection 4.7.1: General Specification of Multigeneration Solids Up Chapter 4: Materials Subsection 4.8.1: General Specification of Biphasic Materials