A new non-smooth model for three dimensional frictional contact problems

This paper presents a new non-smooth model for three dimensional contact problems with Coulomb friction. The problem is formulated exactly as a system of non-smooth equations without employing any external variables or approximation. As compared with the existing models, the present model does not utilize the slip angle as a variable. Therefore, transformation of variables is not required and the formulation is simpler. For solving a three dimensional contact problem, the nodus is to determine the slip direction at the contact nodes because the relative slipping of the contact may occur in any direction on the contact interface. The proposed model solves this problem in a simple manner by formulating it as an equivalent non-smooth equation. Based on the theory of non-smooth analysis, a generalized derivative is introduced to solve the non-smooth equations. Thus, the non-smooth damped Newton method can be implemented directly. The proposed method has been tested using a number of numerical examples.