A key aspect of the problem set up for general contact is that the General Contact Pair always defines the source and destination as the same selection. Hence a more formal definition of source and destination is needed in the following:

With this definition, the destination is identified as the set of boundaries given by the intersection of the boundaries included in the General Contact Pair and a General Contact node. That is, there may be source boundaries that are not part of the destination.

To obtain a consistent formulation, general contact automatically detects if a source of a contact mapping is also part of the destination boundaries and either applies the biased formulation as given by Normal Contact and Tangential Contact with Friction or unbiased formulation as described by Unbiased Formulation and Self Contact. This means that self-contact is automatically accounted for by general contact.

where Λ = 0.5 if the source of the mapping is part of the destination boundaries, otherwise Λ = 1.0. The definition of the contact tractions follows Normal Contact and Tangential Contact with Friction.