Accurate modeling of the cyclic response of structural components constructed of steel with yield plateau Alper Ucak a,⇑ , Panos Tsopelas b a Department of Civil Engineering, The Catholic University of America, Washington DC 20064, United States b Department of Civil Engineering, University of Thessaly, Volos 38334, Greece article info Article history: Received 3 February 2011 Revised 30 May 2011 Accepted 9 October 2011 Keywords: Cyclic plasticity Cyclic loading Structural steel with a yield plateau Buckling abstract A time-independent constitutive model for structural steels with a yield plateau is presented. The model is based on the basic principles of time-independent plasticity. The model couples the nonlinear kine- matic hardening concept with a memory surface in the plastic strain space, and a pseudo memory surface in the deviatoric stress space. A brief description of the constitutive model, which is capable of capturing the response of the material for monotonic, proportional and non-proportional cyclic loading paths are given. The performance of the proposed constitutive model is verified at the structural component level, by means of finite element simulations of large-scale structural columns or bridge pier elements under constant axial load and uni-directional quasi-static cyclic loading. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Recently established design codes require that engineers design structures and/or structural components based on performance objectives. Such requirements are forcing the designers and struc- tural analysts to utilize advanced computational tools in an at- tempt to accurately predict structural behavior in terms of deformations, velocities and accelerations. Structural analysis tools based on finite element method gain popularity among the practi- tioners and have become an indispensable tool, especially in appli- cations involving large amplitude cyclic loading where the material is working well within the inelastic range. In such appli- cations, accurate description of the material response is essential in order to arrive at an accurate and reliable prediction of the member or structural response. Inelastic cyclic characteristics of engineering materials are quantified with cyclic plasticity models, that is, mathematical models based continuum mechanics. Structural steels used in bridge, building, and defense industry have a characteristic yield plateau in their stress–strain response; however, their hysteretic behavior is usually represented by cyclic plasticity models ignoring this aforementioned behavior. Hodge and Minicucci [1], Usami and Ge [2], and Goto et al. [3] using finite element simulations have shown that the dynamic and quasi-static cyclic hysteretic response of structural steel components made of structural steels with a yield plateau cannot be accurately captured, unless the macroscopic response of the base material is correctly modeled. Fig. 1 depicts the generic monotonic stress–plastic strain curve for a structural steel with a yield plateau. For zero to tension loading, after the initial elastic deformation, structural steels with a yield pla- teau show a sharp yield point followed by the yield plateau. The re- sponse along the yield plateau is almost elastic–perfect plastic. Once the loading (strain) amplitude reaches the monotonic hardening threshold, e p sh , the material starts hardening. The hardening curve of the material is usually non-linear with respect to loading (strain) amplitude (Hall [4]). Cyclic response of structural steels with a yield plateau have been experimentally studied (among others) by Lehmann et al. [5], Cofie and Krawinkler [6], Chang and Lee [7], Kowalewski and Sliwowski [8], Sugiura et al. [9], and Peil et al. [10]. Their results show that the monotonic hardening curve will not be representa- tive of the cyclic characteristics of the material. However, for pro- portional loading, there exists one cyclic loading amplitude,  e p sh in Fig. 2, for which the stabilized stress amplitude will coincide with the monotonic stress–strain curve [Fig. 2a]. For fully reversed cyc- lic amplitudes greater than  e p sh , the observed material response is cyclic hardening [Fig. 2b], while for fully reversed amplitudes smaller than  e p sh , the stabilized stress does not exceed the initial yield stress of the virgin material, designated by k [Fig. 2c]. As shown in Fig. 2, regardless of the loading amplitude the stress– plastic strain loops are smooth without any kinks, and exhibit strong Bauschinger effect. The Bauschinger effect, suggests a drop in the initial yield stress under reversed cyclic loading, which is also documented by Lehmann et al. [5] and Kowalewski and Sli- wowski [8]. 0141-0296/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2011.10.015 ⇑ Corresponding author. Tel.: +1 703 999 4247. E-mail addresses: 48ucak@cardinalmail.cua.edu (A. Ucak), tsopelas@uth.gr (P. Tsopelas). Engineering Structures 35 (2012) 272–280 Contents lists available at SciVerse ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct