Theory Manual Version 3.4
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Section 7.7: Tied Multiphasic Contact Up Section 7.7: Tied Multiphasic Contact Subsection 7.7.2: Penalty Method

### 7.7.1 Gap Function

The vector gap function , representing the distance between the contact surfaces, is defined by The premise of a tied interface is that the parametric coordinates of and are both invariants (i.e., they are determined in the reference configuration and remain unchanged over time). The parametric coordinates of correspond to the integration points on , and those of are evaluated once, in the reference configuration, by shooting a ray from the integration point on to intersect . It follows from this premise that If and are not initially conforming, continuity of effective fluid pressure and solute concentration, as well as normal fluid and solute fluxes, will only be enforced within the contact interface; unlike the sliding multiphasic contact interface (Section 7.4↑), ambient conditions are not set automatically on regions of and where a solution for was not found. Therefore, these regions naturally enforce zero fluid and solute flux (impermeable boundary), unless an explicit boundary condition on the effective pressure or solute concentrations are prescribed over those regions.
Section 7.7: Tied Multiphasic Contact Up Section 7.7: Tied Multiphasic Contact Subsection 7.7.2: Penalty Method