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Structural Engineering and Mechanics
  Volume 83, Number 4, August25 2022 , pages 435-449

Evolution of post-peak localized strain field of steel under quasi-static uniaxial tension: Analytical study
Saif L. Altai, Sarah L. Orton and Zhen Chen

    Constitutive modeling that could reasonably predict and effectively evaluate the post-peak structural behavior while eliminating the mesh-dependency in numerical simulation remains to be developed for general engineering applications. Based on the previous work, a simple one-dimensional modeling procedure is proposed to predict and evaluate the post-peak response, as characterized by the evolution of localized strain field, of a steel member to monotonically uniaxial tension. The proposed model extends the classic one-dimensional softening with localization model as introduced by (Schreyer and Chen 1986) to account for the localization length, and bifurcation and rupture points. The new findings of this research are as follows. Two types of strain-softening functions (bilinear and nonlinear) are proposed for comparison. The new failure criterion corresponding to the constitutive modeling is formulated based on the engineering strain inside the localization zone at rupture. Furthermore, a new mathematical expression is developed, based on the strain rate inside and outside the localization zone, to describe the displacement field at which bifurcation occurs. The model solutions are compared with the experimental data on four lowcarbon cylindrical steel bars of different lengths. For engineering applications, the model solutions are also compared to the experimental data of a cylindrical steel bar system (three steel bars arranged in series). It is shown that the bilinear and nonlinear softening models can predict the energy dissipation in the post-peak regime with an average difference of only 4%.
Key Words
    bifurcation; constitutive modeling; low carbon steel; size effect; softening; strain localization
Saif L. Altai, Sarah L. Orton and Zhen Chen: Department of Civil and Environmental Engineering, University of Missouri, Columbia, MO 65211, USA

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