A contactor node ** c** is assumed to be in sticking contact during iteration

- 1.
- The contactor node has penetrated into the target body in iteration
**(**whereas it was not in contact after iteration*i*-1)**(**.*i*-2) - 2.
- The friction resistance during contact is sufficient to prevent sliding.

The constraints to be enforced in the case of sticking contact are

These constraints are enforced through the matrix , and the vectors and . The vector is required to recover the residual from the contact forces resulting from the applied constraints. This residual has been previously computed from the equilibrium of the entire system. Although the contact forces could be directly computed from the values of , but the equilibrium approach gives better accuracy.

Figure (3.4) shows a contactor node ** c** that is in contact with the target element connected to the three nodes

(111) |

where and are the position vector of points

(112) |

Eliminating the penetration vector gives the constraint matrix as

(113) |

where is a scale factor used to scale the constraint matrix and the penetration vector to avoid ill-conditioned coefficient matrix in the left hand side. The matrix equation given as

(114) |

is then assembled to the global system to enforce the sticking contact Condition.