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7.7 Tied Multiphasic Contact
See Section 2.7↑ for a review of multiphasic materials, and  for additional details on contact interfaces involving solutes. The contact interface is defined between surfaces and . Due to continuity requirements on the traction and fluxes, the external virtual work resulting from contact tractions , solvent fluxes and solute fluxes ( may be combined into the contact integral Note that the summation in (7.7-1) is performed only over solutes that are present on both sides of the contact interface. No special treatment is needed for solutes that only belong to one side, since the natural boundary condition for these solutes enforces zero normal flux across the contact interface.
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