On the evaluation of the tangential slip increment in quasi-static beam-to-beam contact problems

Frictional contact models between beams are relevant for the numerical simulation of beam assemblies in various applications such as wiring harnesses, cable bundles or textile manufacturing processes. An essential ingredient of the contact model is the kinematic description of the relative motions of the material particles in the contact zone. In particular, frictional contact models require a quantification of the relative slip motion between the two bodies. This work addresses the definition of the tangential slip increment between geometrically exact beams using the special Euclidean group formalism. This geometric setting guarantees the frame invariance of the results and enables an accurate treatment of complex contact behaviours, such as rolling without slipping interactions.