# Tied Interfaces
Tied interfaces are composed of primary and constrained surfaces. Internally these are broken down to nodes on the constrained side and element (faces) on the primary side. The nodes on the constrained side are connected to the adjacent primary face via a set of constraint equations.
In the case of a quad-4 face this expands to
which forms the constraint equation. This is repeated for all the displacement directions.
The special case is the drilling degree of freedom. As the 2D elements have either no drilling freedom or one which can work quite locally. For this degree of freedom the rotation is linked to the translations of the 2D element. If the node is internal to the element base the rotation of the element as a whole. If the node is on the edge use the rotation of just that edge.
For each element node define a vector
The displacement at the centre of the 2D element is
Then the rotation of the node at a distance
So rotation at