2d Frictional B-Spline Smoothed Mortar Contact Problems Part II: Resolution Phase

Abstract

We detailed in this paper three formulations for the resolution of a contact problem by mortar method. The penalty method is a simple technique which does not introduce new unknowns which can increase the size of the system to be solved. But this formulation suffers of conditioning problems especially when the penalty coefficient becomes very high. The Lagrange multipliers method is more accurate than the penalty formulation. The multiplier λ N represents in the contact surface the exact value of the normal contact effort. This approach requires additional variables which are the Lagrange multiplier in the contact interface nodes. The augmented Lagrange method is a combination between the penalty formulation and the Lagrange multipliers method. The contact constraints are applied by a Lagrange multiplier approached without increasing the problem size. The penalty coefficient in this method has less influence on the quality of the result and the robustness of the solution than in the penalty formulation.