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#### General considerations

Figure 117: Creation of a face-to-face penalty contact element

Figure 118: Integration points resulting from the cutting of one master face (big square) with several slave faces (small, slanted squares)

In the face-to-face penalty contact formulation the spring element which was described in the previous section is now applied between an integration point of a slave face and a master face (spring in Figure 117). The contact force at the integration point is subsequently transferred to the nodes of the slave face. This results in contact spring elements connecting a slave face with a master face (full lines in Figure 117). The integration points in the slave faces are not the ordinary Gauss points. Instead, the master and slave mesh are put on top of each other, the common areas, which are polygons (sides of quadratic elements are approximated by piecewise linear lines), are identified and triangulated. For each triangle a 7-node scheme is used (Figure 118). This can result to up to 100 or more integration points within one slave face. It usually leads to a very smooth pressure distribution. Furthermore, it is now irrelevant which side is defined as master and which as slave. In the present formulation the following approximations are used:

- the linear pressure-overclosure relationship is truly bilinear, i.e. zero for positive clearance and linear for penetration (and not quasi bilinear as for node-to-face penalty). The value of is zero.
- the matching between the slave faces and master faces, the calculation of the resulting integration points and the local normals on the master surface is done once at the start of each increment. This information is not changed while iterating within an increment. The same applies to the calculation of the area for which the slave integration point is representative.
- whether a contact element is active or not is determined in each iteration anew. A contact element is active if the penetration is positive.

Due to the freezing of the match between the slave and master surface within each increment, large deformations of the structure may require small increments.

The contact definition in the input deck is similar to the node-to-face penalty contact except for:

- The contact surfaces (both slave and master) must be face-based.
- On the *CONTACT PAIR card the parameter TYPE=SURFACE TO SURFACE must be specified.
- The SMALL SLIDING parameter on the *CONTACT PAIR card is not allowed.
- The *SURFACE BEHAVIOR card for a linear pressure-overclosure relationship needs only one parameter: the spring constant.
- The *FRICTION card is needed to specify the friction coefficient and the stick slope.

In addition, a new pressure-overclosure relationship is introduced with the name TIED. It can be used to tie surfaces and usually leads to a significantly smoother stress distribution than the MPC's generated by the *TIE option. For the TIED pressure-overclosure relation only two parameters are used: the spring stiffness (, required), and the stick slope (, optional). The friction coefficient is irrelevant.

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