A geometrically exact thin-walled rod model with warping and stress-resultant-based plasticity obtained with a two-level computational approach

Abstract

In this work, we propose an two-level computational approach to enrich a seven degree-of-freedom kinematically exact rod model for thin-walled members, allowing for a simple elastoplastic-hardening constitutive equation. The novelty lies in upper-level description, where the effects of coupled elastoplastic-local geometrical instabilities are characterized in terms of cross-sectional stress resultants and generalized rod strains in a fully 3D context. Torsion-warping degrees of freedom and arbitrary (plastic) failure mode capabilities are present, allowing for the modeling of complex structural behavior in thin-walled members. The lower level is based on a kinematically exact shell or 3D-solid model with usual von Mises plasticity and linear isotropic hardening. At such level, simulations are performed in a pre-process stage, with the resulting equivalent stress-resultant-based hardening plastic parameters directly transferred to the upper-level as input data. No iterative procedure further binding the upper/lower level representations is required. This rather phenomenological approach of incorporating local effects may satisfactorily replicate the overall behavior of thin-walled members consisted of ductile materials, such as, but not only, steel or aluminum beam/column profiles. Numerical solution of the upper-level is carried in the framework of operator split, whereby, the local variables are solved in an element-wise fashion through numerical condensation, thus not adding any extra DOFs to the upper-level. The model is implemented in an in-house finite element program for the analysis of flexible thin structures and is validated against reference solutions.