A modified node-to-segment algorithm passing the contact patch test

Several investigations have shown that the classical one-pass node-to-segment (NTS) algorithms for the enforcement of contact constraints fail the contact patch test. This implies that the algorithms may introduce solution errors at the contacting surfaces, and these errors do not necessarily decrease with mesh refinement. The previous research has mainly focused on the Lagrange multiplier method to exactly enforce the contact geometry conditions. The situation is even worse with the penalty method, due to its inherent approximation that yields a solution affected by a non-zero penetration. The aim of this study is to analyze and improve the contact patch test behavior of the one-pass NTS algorithm used in conjunction with the penalty method for 2D frictionless contact. The paper deals with the case of linear elements. For this purpose, several sequential modifications of the basic formulation have been considered, which yield incremental improvements in results of the contact patch test. The final proposed formulation is a modified one-pass NTS algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method. In other words, this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration.