Covariant description for frictional contact problems

A fully covariant description, based on the consideration of contact from the surface geometry point of view, is used for a consistent formulation of frictional contact conditions. All necessary operations for the description of the contact problems: kinematics, all differential operations etc. are defined in the covariant form in the local coordinate system which corresponds to the closest point procedure. The main advantage is a geometrical structure of the full tangent matrix, which is is subdivided into main, rotational and curvature parts. The consistent linearization of the penalty regularized contact integral leads to a symmetrical tangent matrix in the case of sticking. Representative examples show the effectiveness of the approach for problems where the definition of sticking-sliding zones is necessary as well as for the case of fully developed sliding zones.

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