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Theory Manual Version 3.6
 Subsection 7.7.1: Gap Function Up Section 7.7: Tied Multiphasic Contact Subsection 7.7.3: Discretization 

7.7.2 Penalty Method

Let the tied contact traction be described by the penalty function, where is a penalty factor associated with . Similarly, let where is a penalty factor associated with , and where is a penalty factor associated with . It follows that Given these relations, it can be shown that the directional derivatives of the various terms appearing in the integrand of are where .
 Subsection 7.7.1: Gap Function Up Section 7.7: Tied Multiphasic Contact Subsection 7.7.3: Discretization