Generalized section-section interaction potentials in the geometrically exact beam theory: Modeling of intermolecular forces, asymptotic limit as strain-energy function, and formulation of rotational constraints

The present contribution proposes a universal framework to formulate generalized section–section interaction potentials (SSIP) within the geometrically exact beam theory. By exploiting fundamental kinematic assumption of undeformable cross-sections, an objective (i.e., frame-invariant) description SSIPs via minimal set six (translational and rotational) relative coordinates, either in spatial or material form, is proposed. Based on work-pairing, work-conjugated forces moments, are identified that can be consistently derived from variational principle. Interestingly, it shown hyperelastic stored-energy functions relating deformation measures stress-resultants well-known Simo–Reissner theory also as when considering asymptotic limit small distances rotations between interacting cross-sections. Moreover, proposed problem formulation demonstrated very general nature, thus allowing for translational rotational constraints arbitrarily oriented cross-sections based penalty Lagrange multiplier potential. Possible applications include fiber-based structures materials technical biological systems, where approach allows model short- long-ranged inter-molecular (e.g., electrostatic, van der Waals repulsive steric) interactions fibers complex arrangements coupling different cross-linked polymer chains) matrix phase fiber-reinforced composites).