Uniaxial Nonlocal Formulation for Geometric Nonlinearity–Induced Necking and Buckling Localization in a Steel Bar

Abstract

A nonlocal formulation with the potential to mitigate mesh dependence in fiber models for steel elements is presented. The formulation addresses two common modes of localization in prismatic steel bars: tension necking and compression buckling. These modes are induced by geometric nonlinearity, unlike those addressed by previous nonlocal formulations that focus on localization induced by material softening. Continuum finite element (FE) simulations are conducted to provide benchmark data for development as well as validation of the nonlocal formulation. The nonlocal formulation is implemented through a one-dimensional (1D) line-element-based structural model and has the following features: (1) a uniaxial stress-strain relationship with softening; (2) a length scale representing the necking or buckling process; (3) a volume-averaged nonlocal strain measure that incorporates this length scale; and (4) an imperfection pattern. For both necking and buckling, the nonlocal formulation successfully mitigates mesh dependence shown by the local models, implying that it can reproduce softening load deformation response accurately regardless of mesh discretization. Additionally, comparison to FE benchmark data indicates that the nonlocal formulation is able to characterize the strains inside the localized zone. This latter observation has important implications for simulation of fracture or fatigue that originates in zones of localized strains, such as during cyclic buckling of rebar or local buckling-induced fracture in rolled shapes. Limitations of the study are outlined, identifying challenges for incorporation into fiber models for beam-column elements.