Numerical treatment of nonsmooth frictional beam-to-beam contact

Highly slender structures undergoing large displacements, such as beams, cables or flexible plates are integral parts of most
modern high performance engineering systems. Interest in their virtual simulation has strongly increased in recent years [1].
Modeling their contact interactions is especially challenging since on top of the geometric nonlinearities, unilateral contact
constraints have to be handled. Most works until now focus on smoothed penalty type approaches [2, 3] with the exception
of [4, 5]. In [6], the authors proposed a mortar method for beam-to-beam contact in the static frictionless case. Here, we
present an extension to frictional dynamics in the framework of the nonsmooth generalized-α (NSGA) time integration scheme
following the developments in [7]. It is combined with the beam finite element formulation on the special Euclidean group [8].
The equations of motion, including the contact forces, are expressed in the local frame attached to the beam centerline and are
written on a Lie group resulting in interesting frame invariance properties.