Theory Manual Version 3.4
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Section 7.8: Tied Fluid Interface Up Section 7.8: Tied Fluid Interface Subsection 7.8.2: Gap Functions

### 7.8.1 Contact Integral

See Section 2.11↑ for a review of fluid materials, and [14] for additional details on the FEBio fluid solver. The tied fluid interface is defined between surfaces and . Due to continuity requirements on the viscous traction and normal fluid velocity, the external virtual work resulting from tractions and normal velocities ( may be combined into the tied interface integral To evaluate and linearize , define the covariant basis vectors on each surface as where represents the spatial position of points on , and represent the parametric coordinates of that point. The unit outward normal on each surface is then given by Now the contact integral may be rewritten as where and . The linearization of has the form
Section 7.8: Tied Fluid Interface Up Section 7.8: Tied Fluid Interface Subsection 7.8.2: Gap Functions