  This paper presents an isogeometric finite element formulation for nonlinear
beams with impenetrability constraints, based on the kinematics of Cosserat
rods with unconstrained directors. The beam cross-sectional deformation is
represented by director vectors of an arbitrary order. For the frictionless
lateral beam-to-beam contact, a surface-to-surface contact algorithm combined
with an active set strategy and a penalty method is employed. The lateral
boundary surface of the beam is parameterized by its axis and cross-sectional
boundary curves with NURBS basis functions having at least $C^2$-continuity,
which yields a continuous surface metric and curvature for the closest point
projection. Three-dimensional constitutive laws of hyperelastic materials are
considered. Several numerical examples verify the accuracy and efficiency of
the proposed beam contact formulation in comparison to brick element solutions.
The lateral contact pressure distribution of the beam formulation is in
excellent agreement with the contact pressure of the brick element formulation
while requiring much less degrees-of-freedom.
