A second-order penalty-based node-to-segment contact using the Virtual Element Method

The Node-to-Segment (NTS) method enhanced computational contact mechanics by enabling contact analysis with large deformations with contact location as part of the unknowns. Despite having shortcomings, it is still to this day largely employed by the industry for contact analysis between continuous surfaces due to its low computational cost and scalability, instead of more precise, mathematically sound, but more computationally expensive methods. The method’s persistent relevance inspired attempts at improving its performance, usually for first-order elements. It is well known that NTS is not working well for higher orders due to its topological inconsistency. This work proposes a way of reducing the side-effects of the second order penalty-based Node-to-Segment method without adding complexity to contact detection or formulation. This can be achieved using virtual elements to describe the adjacent continuum, because of a filter effect introduced by the polynomial projection used in stress post-processing, which reduces the stress oscillations resulting from higher order penalty-based Node-to-Segment methods.