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Theory Manual Version 3.6
 Subsubsection 7.1.9.3: Velocities Up Subsection 7.1.9: Sliding-Elastic Subsubsection 7.1.9.5: Penalty Scheme 

7.1.9.4 Coulomb Frictional Contact

This work considers Coulomb frictional contact, with no distinction made between static and kinetic coefficients of friction. Although classical Coulomb friction is the most frequently adopted behavior, it should be noted that other constitutive equations, including micromechanically-inspired formulations which consider local phenomena, have been proposed as well [112, 111]. During frictional contact, the contact traction on the opposing surfaces is determined by the sticking or slipping behavior. For Coulomb friction, the relationship between sticking and slipping is described by a slip criterion , where on the primary surface Here, is the normal component of the contact traction (negative in compression), is the tangential component of the contact traction, and is the friction coefficient. The value of the slip criterion determines the stick-slip status,
Algorithmically, stick and slip are typically based on a predictor-corrector approach derived from an analogy with elastoplasticity [46], leading to constitutive relations for the rate of the traction and thus requiring numerical integration [116]. Variations of this approach have been utilized in differing forms [112, 65, 89].
In contrast, this presentation proposes to treat stick and slip separately, controlled by an exact return mapping based on the slip criterion. The return mapping defines a rule for correcting a calculated traction which exceeds the slip limit and is thus not permissible. Stick will be treated as a special case of a tied interface, whereas in slip the traction will be directly prescribed. The formulation of Coulomb frictional contact is presented for both penalty and augmented Lagrangian regularization schemes.
 Subsubsection 7.1.9.3: Velocities Up Subsection 7.1.9: Sliding-Elastic Subsubsection 7.1.9.5: Penalty Scheme