On a nonlinear rod exhibiting only axial and bending deformations: mathematical modeling and numerical implementation

Abstract In this work, we present the mathematical formulation and numerical implementation of a new model for initially straight, transversely isotropic rods. By adopting configuration space that intrinsically avoids shear deformations by systemically neglecting energetic contribution due to torsion, proposed admits an unconstrained variational statement. Moreover, as natural state rod is trivial one mechanical properties are homogeneous on cross section, need pull-back push-forward operations in totally circumvented. These features impose, however, some smoothness requirements stored energy function be carefully considered when general constitutive models. addition introducing model, propose spatial discretization with finite element method, time integration hybrid, implicit scheme. To illustrate favorable provide results corresponding simulations plane three-dimensional problems investigated static dynamic settings. Finally, put presented ideas suitable context, compare solutions obtained against allows torsion shear.