Theory Manual Version 3.4
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Subsection 2.12.1: FSI Governing Equations Up Chapter 2: Continuum Mechanics Subsection 2.13.1: BFSI Governing Equations

## 2.13 Hybrid Biphasic Material

In FEBio, the standard biphasic material consists of a mixture of intrinsically incompressible solid and fluid constituents, as described in Section 2.5↑. In this standard material, the solid and fluid dynamics are neglected, as well as the fluid viscosity. When a user wishes to consider these dynamics effects, as well as fluid viscosity, they may use a hybrid biphasic material, as described in this section. The complete theoretical framework for such materials can be found in [37]. A hybrid biphasic domain is a mixture of an isothermal compressible viscous fluid and a hyperelastic compressible porous solid whose solid skeleton is intrinsically incompressible. Unlike the fluid-FSI material, here the solid has non-negligible mass density and elasticity, and frictional interactions may occur between the fluid and solid constituents, modeled using a hydraulic permeability (Section 5.7↓). In FEBio, the hybrid biphasic material is called “biphasic-FSI”, since it allows dynamic fluid-structure interactions between this material and a fluid-FSI material, or a solid material. Here, we may abbreviate “biphasic-FSI” as BFSI. For BFSI domains, as with standard biphasic domains, the finite element mesh is defined on the porous solid material. The viscous fluid flows through this mesh, experiencing frictional drag caused by the porous solid. When two BFSI domains are interfaced, or when a BFSI domain is interfaced with a fluid-FSI domain, the pseudo-no slip condition [38] is enforced automatically on those interfaces. When a BFSI domain interfaces with a solid domain, the no-slip boundary condition has to be prescribed explicitly on those interfaces, where applicable.
Subsection 2.12.1: FSI Governing Equations Up Chapter 2: Continuum Mechanics Subsection 2.13.1: BFSI Governing Equations