The node-to-segment algorithm for 2D frictionless contact: Classical formulation and special cases

The so-called node-to-segment (NTS) algorithm is probably the most widely used discretization technique for large deformation contact between surfaces with non-matching meshes. Despite the classical NTS contact element has been available in the literature for a long time, its detailed description appears to be currently disseminated in several papers. Moreover, the classical NTS formulation presents some limitations which are well known but have been the subject of limited investigations. In particular, the algorithm presents severe problems in dealing with some special cases, in which the identification of the master segment related to a slave-node is either ambiguous or impossible. The objectives of this paper are to provide a careful review of the classical formulation, and to propose new techniques for the treatment of the aforementioned special cases. The paper is composed of three parts. In the first one the classical formulation of the NTS algorithm in two dimensions and in the frictionless case is reviewed in detail. The main geometric relationships are presented, and the contact contributions to the stiffness matrix and to the residual vector are derived. The second part is devoted to the treatment of the special cases. Some algorithms specially developed to deal with such cases are illustrated. Finally, the third part presents some numerical examples which show the effectiveness of the proposed algorithms.