Complementarity Problem Formulation of Three-Dimensional Frictional Contact

A general three-dimensional frictional contact problem has been formulated in the form of a complementarity problem in an incremental analysis setting. The derivation is straight forward and very natural. It is shown that the complementarity problem for a three-dimensional case is inherently nonlinear, not like the two-dimensional problem where a linear complementarity problem formulation is possible. The two-dimensional case is a special case of the three-dimensional formulation. Approximate linear complementarity problems of the nonlinear complementarity problem by a Newton approach, or by introducing polyhedral law of friction, have been proposed for efficient numerical implementations.