A special focus on 2D formulations for contact problems using a covariant description

A fully covariant description, based on the consideration of contact conditions especially for the 2D case is proposed. The description is based on a reconsideration of contact kinematics and all necessary operations such as derivatives in a specially chosen curvilinear coordinate system based on a curved geometry in plane. In addition, details of the finite element implementation are presented for the simple linear contact element. Special cases, requiring the update of history variables as well as their careful transfer over the element boundaries are illustrated by numerical examples. With these procedures artificial jumps in the contact forces can be avoide