Improved area regularization technique for penalty-method-based node-to-segment contact analysis

Among numerous approaches that have been presented for computational contact analysis, the node-to-segment (NTS) approach is widely adopted in industrial applications, particularly with the penalty method. However, the pure penalty-method-based NTS approach fails the patch test even with the area regularization (AR) technique. There have been relatively few solutions for this problem compared to those for Lagrange-multiplier-method-based NTS approaches. This paper presents an improved AR technique and attempts to make the penalty-method-based NTS approach pass the patch test. The proposed approach improves the accuracy without the need to introduce additional geometry to the conventional penalty-method-based NTS approach. The entire competence area of a slave node is not directly utilized as a penalty weighting factor. Instead, a part of the competence area is extracted in accordance with the projection from a master node to a slave segment. In a complementary manner, a two-pass algorithm is used for the selected master nodes to achieve segment-wise force/moment equivalence. The results obtained using the proposed approach are introduced in a two-dimensional frictionless context. It is observed that the proposed approach passes the patch test. Furthermore, a significant improvement in accuracy compared to the conventional NTS and NTS-AR approaches is observed. We aim to extend the approach to three-dimensional applications in the future work.