Theory Manual Version 3.6
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Subsection 7.2.1: Contact Integral Up Section 7.2: Biphasic Contact Subsection 7.2.3: Contact Kinematics

### 7.2.2 Biphasic Friction Formulation

An examination of eq.(7.2.1-4) reveals that a contact framework must provide expressions for both the normal fluid flux and the contact traction . For the contact traction, this work implements a Coulomb-like framework for frictional contact [114]. In this framework the relationship between sticking and slipping, and thus the contact traction on the opposing surfaces, is described by a slip criterion , where on the primary surface where Here, is the normal component of the contact traction (negative in compression), is the tangential component of the contact traction, and the effective friction coefficient is given by eq.(7.2.2-1) with no distinction made between static and kinetic coefficients of friction. The user-defined parameter represents the friction coefficient when the fluid pressure has subsided (), whereas the user-defined parameter represents the fraction of the apparent contact area where solid-on-solid contact takes place [16]. The ratio represents the local fluid load support at each point on the contact surface. Since the friction coefficient cannot be negative, the theoretical upper bound on the local fluid load support is . This upper bound is enforced whenever numerical errors produce a greater value of the local fluid load support.
The value of the slip criterion determines the stick-slip status via Following our prior study [114], this work treats stick and slip separately, controlled by an exact return mapping predicated on the value of the slip criterion. The return mapping defines a rule for correcting a calculated stick traction which exceeds the slip limit and is thus not permissible. Stick is treated as a special case of a tied biphasic interface (Section 7.6↓), whereas in slip the traction is directly prescribed as a natural boundary condition. The formulation of biphasic frictional contact is presented for both penalty and augmented Lagrangian regularization schemes.
Subsection 7.2.1: Contact Integral Up Section 7.2: Biphasic Contact Subsection 7.2.3: Contact Kinematics