Consistent memory surface model for plateau and hardening regions

Abstract

Mild steels are frequently used in building structures because of their high strength, productivity, processability, and weldability. One key feature of mild steels is their yield plateau, which is followed by a hardening region in the stress–strain relationship. During large earthquakes, building members can experience a large plastic strain whose amplitude is difficult to predict beforehand. Constitutive equations applicable to the full-range strain field are necessary for accurate structural safety evaluation. This study provides novel constitutive equations for the plateau region, capable of reproducing a yield plateau. A set of hardening constants was proposed to satisfy the consistency condition of the plastic multiplier under any loading pattern. The closed form of the stress–strain relationship was derived to calibrate the material constants. The material constants were calibrated using two types of material test results. The results of the proposed model were consistent with the material test results under cyclic loading at various strain amplitudes. This was validated by comparing the shear buckling and lateral torsional buckling test results of an H-shaped beam with the finite element analysis (FEA) results. The numerical demonstration also highlighted the significance of not only material constitutive laws but also the introduction of residual stress and initial imperfections in reproducing the pre- and post-buckling behaviors. The convergence of the residual force for the proposed model was equivalent to those of the authors’ previous model and the Chaboche model. These results indicate that the proposed model can predict hardening phenomena at the material and structural levels in the plateau and hardening regions.