Industrial applicability of Reissner’s beam theory for large strains in hyperelastic beams

The present work is motivated by an industrial application in which a digital twin is used to control the bending of hyperelastic beam-type structures in real-time. The objective is to assess whether an approximate analytical formulation within the framework of Reissner’s geometrically exact beam theory provides a suitable basis for such applications. To this end, a cantilever beam subjected to a transverse follower force at its free end is investigated. Large deformations are modeled using Hencky’s isotropic hyperelastic material law. The governing equations are derived using a continuum mechanics approach. Since the exact analytical formulation is numerically inefficient, the nonlinear terms are approximated by series expansions, and the resulting equations are solved using Python/SciPy. A numerical study is conducted to evaluate the accuracy and computational efficiency of different expansion orders. The results are further validated by finite element simulations carried out in Abaqus. The outcome is a verified approximate analytical formulation exhibiting a favorable trade-off between accuracy and computational cost, making it suitable for industrial real-time applications.