Geometrically Exact Theory of Contact Interactions–Further Developments and Achievements

The focus of the current contribution is on the development of the unified geometrical formulation of contact algorithms in a covariant form for various geometrical situations of contacting bodies leading to contact pairs: surface-to-surface, line-to-surface, point-to-surface, line-to-line, point-to-line, point-to-point. The construction of the corresponding computational contact algorithms are considered in accordance with the geometry of contact bodies in a covariant form. These forms can be easily discredited within finite element methods independently of order of approximation and, therefore, the result is straightforwardly applied within iso-geometric finite element methods. This approach is recently became known as geometrically exact theory of contact interaction [10]. Application for contact between bodies with isoand anisotropic surface, for contact between cables and curvilinear beams as well as recent development for contact between cables and bodies is straightforward. Recent developments include the improvement of the curve-to-surface (deformable) contact algorithm.