| Matrix or Vector | Geometry | Shape Functions | Integration Points |
|---|---|---|---|
| Stiffness Matrix | Normal Direction | None | None |
| Sliding Direction | None | None |
| Load Type | Distribution |
|---|---|
| Element Temperature | None - average used for material property evaluation |
| Nodal Temperature | None - average used for material property evaluation |
CONTAC12 - 2D Point-to-Point Contact has many aspects also valid for CONTAC52, including normal and sliding force determinations, rigid Coulomb friction (KEYOPT(1) = 1), and the force-deflection relationship shown in Figure 1.2: Force-Deflection Relations for Standard Case.
CONTAC52 may have one of three conditions: closed and stuck, closed and sliding, or open.
If the element is closed and stuck, the element stiffness matrix (in element coordinates) is:
 | (1–61) |
where:
The Newton-Raphson load vector is:
 | (1–62) |
where:
| Fn = normal force across gap (from previous iteration) |
| Fs = sticking force across gap (from previous iteration) |
If the element is closed and sliding in both directions, the element stiffness matrix (in element coordinates) is:
 | (1–63) |
and the Newton-Raphson load vector is the same as in Equation 1–62. For details on the unsymmetric option (NROPT,UNSYM), see CONTAC12 - 2D Point-to-Point Contact
If the element is open, there is no stiffness matrix or load vector.