A kinematically-exact reduced-order rod model for elastoplastic failure in thin-walled members

Abstract

This work profits from a weakly coupled multiscale approach to derive a 7-DOF kinematically-exact reduced-order rod model for thin-walled members (starting from [1]) with a plastic hardening constitutive equation (based on [2]-[3]) that emulates the coupling between local buckling effects and hardening plasticity at material level. The model is implemented in an in-house finite element program for flexible thin structures and shall be validated against reference solutions. The novelty as compared to [2]-[3] is the extension to the fully 3D context, including torsion-warping degrees-of-freedom and arbitrary (plastic) failure mode capabilities, allowing for the modelling of complex structural problems involving thin-walled rod members. Although kinematically-exact rod models are able to detect critical loads and represent postcritical configurations in many common scenarios, issues are bound to emerge when local effects (such as buckling of web and/or flanges) are relevant, especially when they are coupled with plastic deformations. For rod models, the combination of those factors can be satisfactorily represented in a phenomenological way by embedding them on a stress-resultant/crosssectional strains hardening plastic model, instead of enriching the model´s kinematics and related material law. One can employ weakly coupled multiscale modelling to generate constitutive relationships among the different strain and stress in a pre-processing stage. Information about plasticity, loss of geometrical stiffness and local buckling are passed to the macro-scale rod model without increasing the amount of global degrees-of-freedom. Incremental steps of the numerical solution are solved with the split operator, whereby local variables are solved in an element-wise fashion and thus not introduced in the global system. Quadratic convergence of the overall solution procedure is achieved. The coupling among geometrical and hardening effects limits the load bearing capacity of the structural members and determinates the failure load.

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