A torsion-free non-linear beam model

The governing equations of a novel structural model are derived from general balance equations and Lagrangian mechanics. The model represents beam-like slender bodies whose sections can withstand traction and shear forces, plus bending, but no torsional, moments. Although continuum bodies with such a behavior do not exist, multibody systems whose overall response can be described in such a way can be found. In fact, the motivation for this work is the study of certain types of polymers, which can be efficiently modeled as torsion-free rods instead of using long spring-mass chains, for which the proposed continuous model can serve as a basis for efficient finite element discretizations.