  Existing beam contact formulations can be categorized in point contact models
that consider a discrete contact force at the closest point of the beams, and
line contact models that assume distributed contact forces. In this work, it
will be shown that line contact formulations provide accurate and robust
mechanical models in the range of small contact angles, whereas the
computational efficiency considerably decreases with increasing contact angles.
On the other hand, point contact formulations serve as sufficiently accurate
and very efficient models in the regime of large contact angles, while they are
not applicable for small contact angles as a consequence of non-unique closest
point projections. In order to combine the advantages of these basic
formulations, a novel all-angle beam contact (ABC) formulation is developed
that applies a point contact formulation for large contact angles and a
recently developed line contact formulation for small contact angles, the two
being smoothly connected by means of a variationally consistent model
transition. Based on a stringent analysis, two different transition laws are
investigated, optimal algorithmic parameters are suggested and conservation of
energy and momentum is shown. All configuration-dependent quantities are
consistently linearized, thus allowing for their application within implicit
time integration schemes. Furthermore, a step size control of the nonlinear
solution scheme that allows for large displacement increments per time step and
an efficient two-stage contact search based on dynamically adapted search
segments are proposed. A series of numerical test cases is analyzed in order to
verify the accuracy and consistency of the proposed contact model transition
regarding contact force distributions and conservation properties, but also for
quantifying the efficiency gains as compared to standard beam contact
formulations.
