  This contribution proposes the first 3D beam-to-beam interaction model for
molecular interactions between curved slender fibers undergoing large
deformations. While the general model is not restricted to a specific beam
formulation, in the present work it is combined with the geometrically exact
beam theory and discretized via the finite element method. A direct evaluation
of the total interaction potential for general 3D bodies requires the
integration of contributions from molecule or charge distributions over the
volumes of the interaction partners, leading to a 6D integral (two nested 3D
integrals) that has to be solved numerically. Here, we propose a novel strategy
to formulate reduced section-to-section interaction laws for the resultant
interaction potential between a pair of cross-sections of two slender fibers
such that only two 1D integrals along the fibers' length directions have to be
solved numerically. This section-to-section interaction potential (SSIP)
approach yields a significant gain in efficiency, which is essential to enable
the simulation of relevant time and length scales for many practical
applications. In a first step, the generic structure of SSIP laws, which is
suitable for the most general interaction scenario (e.g. fibers with arbitrary
cross-section shape and inhomogeneous atomic/charge density within the
cross-section) is presented. Assuming circular, homogeneous cross-sections, in
a next step, specific analytical expressions for SSIP laws describing
short-range volume interactions (e.g. van der Waals or steric interactions) and
long-range surface interactions (e.g. Coulomb interactions) are proposed. The
validity of the SSIP laws as well as the accuracy and robustness of the general
SSIP approach to beam-to-beam interactions is thoroughly verified by means of a
set of numerical examples considering steric repulsion, electrostatic or van
der Waals adhesion.
