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Theory Manual Version 3.4
 Section 7.5: Tied Contact Up Section 7.5: Tied Contact Subsection 7.5.2: Tied Contact Integral 

7.5.1 Gap Function

Just as in sliding contact, we need to define a gap function that measures the distance between the slave and master surface. In order to do that, we first define the projection of a slave node to the master surface. This definition is similar to that of the sliding interface, except that now the projection is done in the material reference frame. This implies that the projection only needs to be calculated once, at the beginning of the analysis. We can now proceed to the definition of the gap function. An important observation is that the gap function is now a vector quantity since the gap needs to be closed in all direction, not just the normal direction as is the case in sliding contact.
 Section 7.5: Tied Contact Up Section 7.5: Tied Contact Subsection 7.5.2: Tied Contact Integral