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Theory Manual Version 3.6
 Subsection 7.5.1: Gap Function Up Section 7.5: Tied Contact Subsection 7.5.3: Linearization of the Contact Integral 

7.5.2 Tied Contact Integral

With the definition of the gap function at hand (equation (7.5.1-2)), we can define the contribution to the virtual work equation from the tied contact reaction forces. Here, is the reaction force that enforces the constraint . Since we anticipate the use of an augmented Lagrangian formalism, we can write this reaction force as follows, The vector quantity is the Lagrangian multiplier and is a penalty factor.
 Subsection 7.5.1: Gap Function Up Section 7.5: Tied Contact Subsection 7.5.3: Linearization of the Contact Integral