Large penetration algorithm for 3D frictionless contact problems based on a covariant form

A 3D extension of the so-called large penetration algorithm is presented based on the consideration of contact from the surface geometry point of view using a covariant contact description in the local surface coordinate system. This enables to achieve the specific structure of the tangent matrix in a straightforward fashion for the large penetration scheme. Representative examples with contact and bending of shells modeled with linear and quadratic elements over some classical second order geometrical figures serve to show the efficiency of the combination of the covariant approach with the large penetration scheme.