3D frictionless contact problems with large load-steps based on the covariant description for higher order approximation

Based on the consideration of contact from the surface geometry point of view using a covariant contact description in the local surface coordinate system a 3D extension of the so-called large penetration algorithm is presented. Within the Node-To-Surface (NTS) approach this scheme allows the computation with larger load increments than within a usual consistent linearization, see [2]. The required specific structure of the tangent matrix for this 3D scheme is found in a straightforward fashion using the covariant contact description. In order to show the efficiency of the scheme for further approaches like e.g. the Surface-To-Analytical-Surface (STAS) examples with contact, bending and sliding of shells modeled with elements of quadratic approximation, are presented. Furthermore a comparison regarding the efficiency for both considered approaches, NTS and STAS, is presented.