Dynamic simulation of frictional contact between slender beams via cone complementarity formulations

Beam-to-beam contact with friction is a fundamental phenomenon in the dynamic analysis of slender structures, particular in applications involving large deformation and complex contact interactions. In this study, a robust computational framework is proposed for solving beam contact problems with friction based on the theory of cone complementarity problems for both point-to-point and line-to-line contact cases. The thin beams are modeled using the geometrically exact Kirchhoff beam theory, which captures large displacements and rotations without shear deformation. A unified contact detection algorithm is elaborated to consistently identify both point-to-point and line-to-line contact. Contact and frictional constraints are enforced through cone complementarity formulations, providing a unified and physically consistent treatment of unilateral contact and Coulomb friction. For discretization, the point-to-point contact model is used for the cases where the contact region is small enough to be approximated by a point, while the mortar method is employed for line-to-line contact to ensure variational consistency. The dynamic equilibrium equations are integrated using the generalized-a method, in which the cone complementarity problems are efficiently solved via an alternating direction method of multipliers. The accuracy, efficiency, and versatility of the proposed method are demonstrated through six numerical examples.