Kinematic Hardening Model Comparison of Square Hollow Section Under Cyclic Bending


Aniendhita Rizki Amalia
Kenshi Ochi


This study compares the different linearity of the kinematic hardening model of the Square Hollow Section (SHS) under cyclic bending loading. Four specimens of a simple support beam cyclically tested in previous research are listed as hot-rolled, hot-finished, and two cold-formed. Using the bilinear, multilinear, and Chaboche models, each specimen is modeled in kinematic hardening. The variables or node sets for each linearity model are estimated using tensile test data, and Chaboche variables are obtained using the least-square fitting method. Each linearity model for each specimen is built-in FEA using a shell model. The numerical model applied the same cyclic loading history as the previous test. The numerical analysis comparison concluded that Chaboche and the multilinear kinematic model generate the expected result fitted to test hysteresis of cold-formed one and cold-formed 2 SHS, but the bilinear models are not fitted. Moreover, all kinematic models are not fit for the hot-rolled and hot-finished SHS compared to the test hysteresis. So, for hot-rolled and hot-finished SHS, the combined hardening is suggested; there is a possibility it is because of the lower yield ratio that both sections have. Overall, during a cyclic bending analysis of cold-formed SHS, multilinear or Chaboche models are preferable if the data is limited.


How to Cite
Amalia, A. R. ., & Ochi, K. (2022). Kinematic Hardening Model Comparison of Square Hollow Section Under Cyclic Bending . Applied Research on Civil Engineering and Environment (ARCEE), 3(02), 88–103.


  1. ANSYS, I. (2005). Advanced Structural Nonlinearities. ANSYS 9.0., 002205(First Edition).
  2. Ansys inc. (2010). Mechanical APDL Element Reference. 15317(November), 9.
  3. Arrayago, I., & Real, E. (2015). Experimental Study on Ferritic Stainless Steel RHS and SHS Cross-sectional Resistance Under Combined Loading. Structures, 4, 69–79.
  4. Bhashyam, G. R. (2002a). ANSYS Mechanical — A Powerful Nonlinear Simulation Tool. September.
  5. Bhashyam, G. R. (2002b). ANSYS Mechanical — A Powerful Nonlinear Simulation Tool (Issue September). ANSYS, Inc.
  6. Bouchenot, T., Felemban, B., Mejia, C., & Gordon, A. P. (2016). Application of Ramberg-Osgood plasticity to determine cyclic hardening parameters. American Society of Mechanical Engineers, Power Division (Publication) POWER, 2016-January (June 2017).
  7. EN 10210 Hot Finished Structural Hollow Sections of Non-Alloy and Fine Grain Steels, (2006).
  8. EN 10219 Cold-formed welded structural hollow sections of non-alloy and fine grain steels, (2006).
  9. Budaházy, V., & Dunai, L. (2013). Parameter-refreshed Chaboche model for mild steel cyclic plasticity behaviour. Civil Engineering, 57(2), 139–155.
  10. Chaboche, J. L. (1986). Time-independent constitutive theories for cyclic plasticity. International Journal of Plasticity, 2(2), 149–188.
  11. Chaboche, J. L. (2008). A review of some plasticity and viscoplasticity constitutive theory. International Journal of Plasticity, 24, 1642–1693.
  12. Chaboche, J. L., & Rousselier, G. (1983). On the plastic and viscoplastic constitutive equation. International Journal of Pressure Vessel Piping, 105(2), 153–158.
  13. Chavan, V. B., Nimbalkar, V. N., & Jaiswal, A. P. (2014). Economic Evaluation of Open and Hollow Structural Sections in Industrial Trusses. International Journal of Innovative Research in Science, Engineering and Technology, 3(2), 9554–9565.
  14. Crișan, A. (2016). Material Calibration for Static Cyclic Analyses. 13(2), 43–58.
  15. Fadden, M. (2013). Cyclic Bending Behavior of Hollow Structural Sections and their Application in Seismic Moment Frame Systems. 297.
  16. Fadden, M., & McCormick, J. (2014). Finite element model of the cyclic bending behavior of hollow structural sections. Journal of Constructional Steel Research, 94, 64–75.
  17. Fang, H., & Chan, T. M. (2019). Resistance of Axially Loaded Hot-finished S460 and S690 Steel Square Hollow Stub Columns at Elevated Temperatures. Structures, 17(November 2018), 66–73.
  18. Gardner, L., & Yun, X. (2018). Description of stress-strain curves for cold-formed steels. Construction and Building Materials, 189, 527–538.
  19. Gardner, L., Yun, X., Macorini, L., & Kucukler, M. (2017). Hot-Rolled Steel and Steel-Concrete Composite Design Incorporating Strain Hardening. Structures, 9, 21–28.
  20. Gkantou, M., Theofanous, M., & Baniotopoulos, C. (2018). Plastic design of hot-finished high strength steel continuous beams. Thin-Walled Structures, 133, 85–95.
  21. Imaoka, S. (2008). Chaboche Nonlinear Kinematic Hardening Model. Internal Report, (1), 1–15.
  22. Jia, L. J., & Kuwamura, H. (2014). Prediction of cyclic behaviors of mild steel at large plastic strain using coupon test results. Journal of Structural Engineering, 140(2).
  23. Lakshminarayanan, R., & Technologies, S. M. (2014). CAE Simulation of Non-Linear Analysis - Modeling of Material Model using Isotropic Material Hardening Law Simulation of Non-Linear Analysis in ANSYS Introduction : January 2006.
  24. Lin, J., Zhu, T., & Zhan, L. (2011). Constitutive equations for modelling superplastic forming of metals. In Superplastic Forming of Advanced Metallic Materials. 154–183. Woodhead Publishing.
  25. Ma, J. L., Chan, T. M., & Young, B. (2019). Cold-Formed High-Strength Steel Rectangular and Square Hollow Sections under Combined Compression and Bending. In Journal of Structural Engineering (United States), 145(12).
  26. Matshusita, K., Iwata, D., & Ochi, K. (2019). Finite Element Analysis of The Cyclic Behavior of Circular Tubular Braces. Proceedings Ofthe 17th International Symposium on Tubular Structures., 574–581. 083-cd 5740
  27. Meng, X., & Gardner, L. (2020). Testing of hot-finished high strength steel SHS and RHS under combined compression and bending. Thin-Walled Structures, 148(June 2019), 106262.
  28. Nagai, T., & Ochi, K. (2019). Influence of material on inelastic behaviour and local buckling of SHS Members under cyclic loading. Nordic Steel Copenhagen, 3(3–4), 493–498.
  29. Nip, K. H., Gardner, L., Davies, C. M., & Elghazouli, A. Y. (2010). Extremely low cycle fatigue tests on structural carbon steel and stainless steel. Journal of Constructional Steel Research, 66(1), 96–110.
  30. Patillo, P. D. (2018). Yield and Inelastic Behavior. In Elements of Oil and Gas Well Tubular Design. 151–195. Gulf Professional Publishing.
  31. Resapu, R., & Perumahanthi, L. R. (2020). Numerical study of bilinear isotropic & kinematic elastic–plastic response under cyclic loading. Materials Today: Proceedings, xxxx.
  32. Terada, S., Ochi, K., Nagaoka, T., Structures, T., Gardner, X. I. V, & Terada, S. (2012). Rotation capacity and ductility of square hollow sections : A comparison between cold-formed and hot-finished sections. The 13th International Symposium of Tubular Structure, 765–771.
  33. Tsuchiya, K., & Ochi, K. (2016). Behavior of rectangular HSS members under cyclic loading -A comparison between cold-formed , hot-rolled and hot-finished sections.
  34. Wang, J., Afshan, S., Gkantou, M., Theofanous, M., Baniotopoulos, C., & Gardner, L. (2016a). Flexural behaviour of hot-finished high strength steel square and rectangular hollow sections. Journal of Constructional Steel Research, 121(June), 97–109.
  35. Wang, J., Afshan, S., Gkantou, M., Theofanous, M., Baniotopoulos, C., & Gardner, L. (2016b). Flexural behaviour of hot-finished high strength steel square and rectangular hollow sections. Journal of Constructional Steel Research, 121, 97–109.
  36. Wu, H., Meggiolaro, M. A., & de Castro, J. T. P. (2016). Computational implementation of a non-linear kinematic hardening formulation for tension–torsion multiaxial fatigue calculations. International Journal of Fatigue, 91, 304–312.
  37. Yun, X., & Gardner, L. (2017). Stress-strain curves for hot-rolled steels. Journal of Constructional Steel Research, 133(September), 36–46.
  38. Yun, X., Wang, Z., & Gardner, L. (2020). Structural performance and design of hot-rolled steel SHS and RHS under combined axial compression and bending. Structures, 27(June), 1289–1298.
  39. Zhao, O., Gardner, L., & Young, B. (2016). Behaviour and design of stainless steel SHS and RHS beam-columns. Thin-Walled Structures, 106, 330–345.