Constitutive Modeling of Structural Steels: Nonlinear Isotropic/Kinematic Hardening Material Model and Its Calibration
Publication: Journal of Structural Engineering
Volume 147, Issue 4
Abstract
Numerical models of structural components that deteriorate primarily due to geometric instabilities under multiaxis cyclic loading are sensitive to both the assumed geometric imperfections and the nonlinear material model assumptions. Therefore, the accuracy of the constitutive model is a desirable feature in finite-element simulations. However, the classic Voce-Chaboche metal plasticity model, ubiquitous among commercial finite-element software, is found to underestimate the initial yield stress in structural steels by about 10%–30% when calibrated to minimize the overall difference in strain energy between the model and test data of load protocols representative of earthquake loading. This paper proposes a refined version of the Voce-Chaboche material model. When compared with the original model, the updated one improves the prediction of the initial yield stress, can simulate initial yield plateau behavior, and better estimates experimental cyclic stress-strain data. Constraints on the model parameters are established, a calibration procedure is developed, and model parameters are proposed for nine structural steels used worldwide. Source code for the material model is also made publicly available. A case study demonstrates that steel component behavior is sensitive to subtle differences in the material response that arise between the Voce-Chaboche and the proposed material models.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository or online in accordance with funder data retention policies. This includes the following: the code used for the calibration procedure available in RESSPyLab (de Castro e Sousa et al. 2019), the finite-element models used for validation, and the implemented material models available in the study by Hartloper (2019).
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. This includes the following: the finite-element models used in the case study section and the uniaxial stress-strain data used for the calibration of parameters in Tables 1 and 2.
Acknowledgments
This study is based on work supported by the École Polytechnique Fédérale de Lausanne (EPFL) and by the Swiss National Science Foundation (Project No. 200021_188476). The financial support is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the view of sponsors.
References
ABAQUS. 2014. ABAQUS standard and ABAQUS documentation for version 6.14. Providence, RI: Dassault Systèmes Simulia.
AISC. 2016. Seismic provisions for structural steel buildings. ANSI/AISC 341-16. Chicago: AISC.
Armstrong, P. J., and C. Frederick. 1966. A mathematical representation of the multiaxial Bauschinger effect. London: Central Electricity Generating Board, Berkeley Nuclear Laboratories.
ASTM. 2015. Standard specification for structural steel shapes. ASTM A992/A992M-11. West Conshohocken, PA: ASTM.
ASTM. 2018. Standard terminology relating to steel, stainless steel, related alloys, and ferroalloys. ASTM A941-18. West Conshohocken, PA: ASTM.
ATC (Applied Technology Council). 2017. Guidelines for nonlinear structural analysis and design of buildings. Part IIa: Steel moment frames. Gaithersburg, MD: National Institute of Standards and Technology.
ATC (Applied Technology Council). 2018. “ATC-106-1 beam column blind prediction contest.” Accessed September 9, 2019. https://www.atcouncil.org/atc-106-blind-contest.
Bierlaire, M. 2015. Optimization: Principles and algorithms. Lausanne, Switzerland: EPFL Press.
Budaházy, V., and L. Dunai. 2013. “Parameter-refreshed Chaboche model for mild steel cyclic plasticity behaviour.” Period. Polytech. Civ. Eng. 57 (2): 139–155. https://doi.org/10.3311/PPci.7170.
Byrd, R. H., M. E. Hribar, and J. Nocedal. 1999. “An interior point algorithm for large-scale nonlinear programming.” SIAM J. Optim. 9 (4): 877–900. https://doi.org/10.1137/S1052623497325107.
CEN (European Committee for Standardization). 1993. Structural steel I and H sections: Tolerances on shape and dimensions. EN 10034:1993. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2005a. Design of steel structures part 1-1: General rules and rules for buildings. EN 1993-1-1. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2005b. Hot rolled products of structural steels part 2: Technical delivery conditions for non-alloy structural steels. EN 10025-2. Brussels, Belgium: CEN.
Chaboche, J. L., K. D. Van, and G. Cordier. 1979. “Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel.” In Proc., 5th Int. Conf. on Structural Mechanics in Reactor Technology. Amsterdam, Netherlands: North-Holland Publishing.
Cofie, N. G., and H. Krawinkler. 1985. “Uniaxial cyclic stress-strain behavior of structural steel.” J. Eng. Mech. 111 (9): 1105–1120. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:9(1105).
Conn, A. R., N. I. M. Gould, and P. L. Toint. 2000. Trust region methods: MOS-SIAM series on optimization. Philadelphia, PA: Society for Industrial and Applied Mathematics.
Cottrell, A. H., and B. A. Bilby. 1949. “Dislocation theory of yielding and strain ageing of iron.” Proc. Phys. Soc. London, Sect. A 62 (1): 49–62. https://doi.org/10.1088/0370-1298/62/1/308.
Cravero, J., A. Elkady, and D. G. Lignos. 2020. “Experimental evaluation and numerical modeling of wide-flange steel columns subjected to constant and variable axial load couple with lateral drift demands.” J. Struct. Eng. 146 (3): 04019222. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002499.
de Castro e Sousa, A., A. R. Hartloper, and D. G. Lignos. 2019. “RESSPyLab version 1.0: Python tools for structural steel research.” Accessed December 21, 2020. https://pypi.org/project/RESSPyLab/.
de Castro e Sousa, A., and D. G. Lignos. 2017. Residual stress measurements of European hot-rolled I-shaped steel profiles. Lausanne, Switzerland: Resilient Steel Structures Laboratory (RESSLab), EPFL.
de Castro e Sousa, A., Y. Suzuki, and D. Lignos. 2020. “Consistency in solving the inverse problem of the Voce-Chaboche constitutive model for plastic straining.” J. Eng. Mech. 146 (9): 04020097. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001839.
Elkady, A. 2016. “Collapse risk assessment of steel moment resisting frames designed with deep wide-flange columns in seismic regions.” Ph.D. thesis, Dept. of Civil Engineering and Applied Mechanics, McGill Univ.
Elkady, A., and D. G. Lignos. 2015. “Analytical investigation of the cyclic behavior and plastic hinge formation in deep wide-flange steel beam-columns.” Bull. Earthquake Eng. 13 (4): 1097–1118. https://doi.org/10.1007/s10518-014-9640-y.
Elkady, A., and D. G. Lignos. 2018a. “Full-scale testing of deep wide-flange steel columns under multiaxis cyclic loading: Loading sequence, boundary effects, and lateral stability bracing force demands.” J. Struct. Eng. 144 (2): 04017189. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001937.
Elkady, A., and D. G. Lignos. 2018b. “Improved seismic design and nonlinear modeling recommendations for wide-flange steel columns.” J. Struct. Eng. 144 (9): 04018162. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002166.
Fell, B. V., A. M. Kanvinde, G. G. Deierlein, and A. T. Myers. 2009. “Experimental investigation of inelastic cyclic buckling and fracture of steel braces.” J. Struct. Eng. 135 (1): 19–32. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:1(19).
Fogarty, J., and S. El-Tawil. 2016. “Collapse resistance of steel columns under combined axial and lateral loading.” J. Struct. Eng. 142 (1): 04015091. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001350.
Grigoriou, V., and D. G. Lignos. 2017. Characterization of the cyclic hardening properties of European steels. Lausanne, Switzerland: Resilient Steel Structures Laboratory (RESSLab), EPFL.
Haidemenopoulos, G. N. 2018. Physical metallurgy: Principles and design. Boca Raton, FL: CRC Press.
Hall, E. O. 1970. Yield point phenomena in metals and alloys. New York: Plenum Press.
Hartloper, A. R. 2019. “UVC_MatMod: Updated Voce-Chaboche (UVC) material model for structural steels.” Accessed November 22, 2019. https://github.com/ahartloper/UVC_MatMod.
Hartloper, A. R., A. de Castro e Sousa, and D. G. Lignos. 2019. A nonlinear isotropic/kinematic hardening model for materials with discontinuous yielding. Lausanne, Switzerland: Resilient Steel Structures Laboratory (RESSLab), EPFL.
Hartloper, A. R., and D. G. Lignos. 2019. Measurement and identification of imperfections in steel wide-flange cross-sections using point cloud data. Lausanne, Switzerland: Resilient Steel Structures Laboratory (RESSLab), EPFL.
Hassan, T., and S. Kyriakides. 1992. “Ratcheting in cyclic plasticity. Part I: Uniaxial behavior.” Int. J. Plast. 8 (1): 91–116. https://doi.org/10.1016/0749-6419(92)90040-J.
Hopperstad, O. S., and S. Remseth. 1995. “A return mapping algorithm for a class of cyclic plasticity models.” Int. J. Numer. Methods Eng. 38 (4): 549–564. https://doi.org/10.1002/nme.1620380404.
Hsiao, P.-C., D. E. Lehman, and C. W. Roeder. 2012. “Improved analytical model for special concentrically braced frames.” J. Constr. Steel Res. 73 (Jun): 80–94. https://doi.org/10.1016/j.jcsr.2012.01.010.
Hu, F., G. Shi, and Y. Shi. 2018. “Constitutive model for full-range elasto-plastic behavior of structural steels with yield plateau: Formulation and implementation.” Eng. Struct. 171 (Sep): 1059–1070. https://doi.org/10.1016/j.engstruct.2016.02.037.
Imanpour, A., R. Tremblay, A. Davaran, C. D. Stoakes, and L. A. Fahnestock. 2016. “Seismic performance assessment of multitiered steel concentrically braced frames designed in accordance with the 2010 AISC seismic provisions.” J. Struct. Eng. 142 (12): 04016135. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001561.
Jones, E., T. Oliphant, and P. Peterson. 2001. “SciPy: Open source scientific tools for Python.” Accessed November 19, 2018. http://www.scipy.org/.
Kalochairetis, K. E., and C. J. Gantes. 2011. “Numerical and analytical investigation of collapse loads of laced built-up columns.” Comput. Struct. 89 (11): 1166–1176. https://doi.org/10.1016/j.compstruc.2010.10.018.
Kanno, R. 2016. “Advances in steel materials for innovative and elegant steel structures in Japan—A review.” Struct. Eng. Int. 26 (3): 242–253. https://doi.org/10.2749/101686616X14555428759361.
Kaufmann, E. J., B. Metrovich, and A. W. Pense. 2001. Characterization of cyclic inelastic strain behavior on properties of A572 Gr. 50 and A913 Gr. 50 rolled sections. Bethlehem, PA: ATLSS, Lehigh Univ.
Lemaitre, J., and J.-L. Chaboche. 1990. Mechanics of solid materials. Cambridge, UK: Cambridge University Press.
Lignos, D. G., A. R. Hartloper, A. Elkady, G. G. Deierlein, and R. O. Hamburger. 2019. “Proposed updates to the ASCE 41 nonlinear modeling parameters for wide-flange steel columns in support of performance-based seismic engineering.” J. Struct. Eng. 145 (9): 04019083. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002353.
Lubliner, J. 2008. Plasticity theory. New York: Dover.
Mahan, M., Y. F. Dafalias, M. Taiebat, Y. Heo, and S. K. Kunnath. 2011. “SANISTEEL: Simple anisotropic steel plasticity model.” J. Struct. Eng. 137 (2): 185–194. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000297.
McKenna, F. T. 1997. “Object-oriented finite element programming: Frameworks for analysis, algorithms and parallel computing.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of California.
Neilsen, M., and H. Schreyer. 1993. “Bifurcations in elastic-plastic materials.” Int. J. Solids Struct. 30 (4): 521–544. https://doi.org/10.1016/0020-7683(93)90185-A.
Ohno, N. 1982. “A constitutive model of cyclic plasticity with a nonhardening strain region.” J. Appl. Mech. 49 (4): 721–727. https://doi.org/10.1115/1.3162603.
Schafer, B. W., Z. Li, and C. D. Moen. 2010. “Computational modeling of cold-formed steel.” Thin-Walled Struct. 48 (10): 752–762. https://doi.org/10.1016/j.tws.2010.04.008.
Simo, J. C., and T. J. R. Hughes. 1998. “Computational inelasticity.” In Interdisciplinary applied mathematics. New York: Springer.
Sowerby, R., D. Uko, and Y. Tomita. 1979. “A review of certain aspects of the Bauschinger effect in metals.” Mater. Sci. Eng. 41 (1): 43–58. https://doi.org/10.1016/0025-5416(79)90043-0.
Suzuki, T., Y. Yoshida, Y. Shimura, Y. Suzuki, S. Kubota, and M. Nagata. 2008. Development of building structural steel with high yield ratio and high yield point leading to innovative steel structural system. Tokyo: Nippon Steel.
Suzuki, Y. 2018. “Earthquake induced collapse of steel moment resisting frames with conventional and high performance steel columns.” Ph.D. thesis, Dept. of Civil Engineering and Applied Mechanics, McGill Univ.
Ucak, A., and P. Tsopelas. 2011. “Constitutive model for cyclic response of structural steels with yield plateau.” J. Struct. Eng. 137 (2): 195–206. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000287.
Voce, E. 1948. “The relationship between stress and strain for homogeneous deformation.” J. Inst. Met. 74: 537–562.
Yoshida, F., and T. Uemori. 2002. “A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation.” Int. J. Plast. 18 (5): 661–686. https://doi.org/10.1016/S0749-6419(01)00050-X.
Young, B. W. 1972. “Residual stresses in hot rolled members.” In Vol. 23 of International colloquium on column strength, 25–38. Paris: International Association for Bridge and Structural Engineering.
Ziemian, R. D., J. C. Batista Abreu, M. D. Denavit, and T.-J. L. Denavit. 2018. “Three-dimensional benchmark problems for design by advanced analysis: Impact of twist.” J. Struct. Eng. 14 (12): 04018220. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002224.
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Published In
Journal of Structural Engineering
Volume 147 • Issue 4 • April 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 6, 2019
Accepted: Nov 23, 2020
Published online: Jan 30, 2021
Published in print: Apr 1, 2021
Discussion open until: Jun 30, 2021
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