Modeling reinforced concrete structures under severe cyclic loading incorporating plasticity and damage models

Abstract

Recent advances in the field of computation technology and increased requirements inthe field of earthquake engineering have led to the development and implementation ofhighly efficient beam‐column elements capable of tracking the hysteretic behavior ofReinforced Concrete (RC) structures. The aim of this dissertation is to model beam‐columnbehavior in a computationally effective manner, reliably revealing the overall response of RCmembers subjected to intensive cyclic loading. In this respect, plasticity and damage areconsidered in the predominant longitudinal direction allowing for the derivation of a fiberfinite element model which is formulated on the basis of the two‐field Hellinger‐Reissnerenergy principle. Following this methodology, a uniaxial local stress‐strain constitutive relation for steelrebars is developed, which is based on a combined nonlinear kinematic and isotropichardening law. The model also incorporates Bauschinger effect, yield plateau and is capableof addressing the overshooting problem after short reversals, maintaining full memory ofthe loading path. In addition, the effect of inelastic buckling of longitudinal rebars, whichbecomes essential at later stages of intensive cyclic loading, is incorporated. The rebar cross‐section is considered discretized into fibers, each one following the derived stress‐strainuniaxial law. The buckling curve is analytically determined while equilibrium is imposed onthe deformed configuration. Finally, the proposed formulation is verified with existingexperimental data of longitudinal rebars under cyclic loading exhibiting inelastic buckling. In addition, a smooth plasticity‐damage model is developed for concrete, accounting forunilateral compressive and tensile behavior, nonlinear unloading and crack‐closurephenomena. Softening and stiffness degradation phenomena are handled through a scalardamage‐driving variable, which is a function of total strain. Smoothening of the incrementaldamage behavior is achieved following similar steps to the steel formulation, thus exploitingthe common mathematical structure of classical plasticity and damage mechanics. Concretemodel is validated in terms of experimental results on concrete specimens under imposedcyclic strain histories and it can efficiently address core crushing and cover spalling failuremechanisms.The uniaxial models for concrete and rebar are employed to derive a fiber beam‐columnelement which is used to assemble the numerical model of frame structures. Following thetwo‐field mixed approach the state determination of the proposed element is numericallyinvestigated following two alternative methods that provide identical results, i.e. alinearization method and a solution in state‐space form. Global solution of the entire systemin the linearization method is established using a standard Newton‐Raphson numericalscheme, which in the inner loop incorporates the evolution equations of all fibers elevatedat section, element and structural level. Also, cover spalling, which triggers the inelasticbuckling of longitudinal reinforcing bars, is detected as soon as the damage variable of theadjacent concrete fibers exceeds a threshold value. Numerical results that compare wellwith existing experimental data on RC structures are presented demonstrating the accuracy and efficacy of the proposed formulation.