Constitutive modeling, implementation and validation
Low-Yield-Point Steel (LYP steel) possesses mechanic characteristics of stable low yield strength, favorable fatigue behavior and excellent ductility. As such, LYP is widely considered as an optimal material for seismic-resistant members credit to its promising hysteretic energy-dissipating capacity. Nonetheless, this type of steel exhibits complicated nonlinear elasto-plastic behavior under cyclic deformation, which makes it challenging to accurately describe the material’s stress-strain response for application in engineering structures. In fact, a thorough review of published literature reveals that LYP steel exhibits three crucial phenomenological features when subjected to reversed loading: i.e. significant working hardening with accumulation of plastic strain, strain range and loading history dependence, and idiosyncratic cyclic softening with the change in hysteresis loops’ shape. All these three are deemed important in numerical simulations and thereby it demands a sophisticated constitutive model for reasonably predicting the hysteresis responses. Contemporarily, although plentiful commercial finite element (FE) software packages, such as ABAQUS, MARC and ANSYS, etc., have commonly provided a general nonlinear combined hardening model for metal cyclic plasticity, none of them is able to fully capture all the aforementioned nonlinear features of LYP steel.
In a recent publication, the strengths and weaknesses of different plasticity models were reviewed with more detail, and a modified constitutive model based on the combined hardening laws proposed for exquisitely describing the cyclic behavior of LYP160 steel. This bore remarkable results; however, it was seen that with the increasing complexity of phenomena modeled, the number of constitutive equations and nonlinearity in mathematical models tend to increase significantly, thereby casting additional difficulties on robust implementation procedures. On this account, researchers from Tsinghua University and Beihang University: Dr. Chen Wang, Dr. Jian-sheng Fan, Dr Li-yan Xu and Dr. Xin Nie, proposed to implement and validate the model as elaborated by Xu LY et al 2016. Their work is currently published in the research journal, Engineering Structures.
In their approach, they first reviewed the mathematical formulation, where each constitutive equation was illustrated in line with the hysteretic characteristics of LYP steel. Subsequently, a modified radial return algorithm was proposed to realize the fully implicit stress update procedures in general case, where stepwise derivation was presented in detail for both the scalar equation with respect to plastic flow increment and the consistent tangent moduli. Moreover, the constitutive model was implemented into the general finite element analysis package ABAQUS utilizing the user subroutine UMAT.
The authors reported that the modified algorithm was universally suitable for J2 plasticity model adopting A-F hardening law. In fact, the modified algorithm was seen to retain the collinearity of three intermediate stress states on account of evanescence term and helped resume the derivation for the classical-form scalar equation. Overall, the comparison of simulation and experimental results indicated that the model was capable of accurately describing all cyclic features – especially the multi-stage evolutionary cyclic softening with flattening effect – of LYP steel, and predicting the failure or damage mode of specimens.
In summary, the study developed a computational procedure using the modified radial return algorithm to implement a proposed sophisticated model into finite element application. In the study, a number of numerical examples on LYP steel were given to validate the utility and robustness of the developed model. In a statement to Advances in Engineering, Professor Li-Yan Xu pointed out that the close fit between simulations and experimental results proved the developed model was capable of accurately describing the nonlinear cyclic hardening and softening properties with memory effect for LYP steel, which showed that the model provides a powerful tool for structural seismic simulation and analysis.
Chen Wang, Jian-Sheng Fan, Li-Yan Xu*, Xin Nie. Cyclic hardening and softening behavior of the low yield point steel: Implementation and validation. Engineering Structures, volume 210 (2020) 110220.
Li-Yan Xu, Xin Nie, Jian-Sheng Fan*, Mu-Xuan Tao, Rang Ding. Cyclic hardening and softening behavior of the low yield point steel BLY160: Experimental response and constitutive modeling. International Journal of Plasticity, 2016, 78: 44-63.