Frictionless line-to-line contact: Comparison of mortar and unbiased formulation in combination with Lagrange-multiplier and penalty method

Recent developments in the beam-to-beam contact mechanics have prompted us to investigate further into the relations between different formulations and contact-force models. Specifically we address in this paper the recently developed mortar method for beams and develop its variant based on the penalty method. This allows an in-depth comparison between the two formulations. Furthermore, we design an unbiased approach and introduce a new discretisation technique developed specifically for this method. The unbiased line-to-line method is also combined both with the Lagrange-multiplier and the penalty method. All developed elements have been tested using the same examples to provide an objective comparison between formulations in terms of robustness and computational cost.