Plastic – Damage Modeling of RC Beams under Torsion

Among four basic load-bearing mechanisms of reinforced concrete structural elements, namely, axial, flexure, shear and torsion, only the latter is truly a three-dimensional problem. Consequently, studies of pure torsion serve to verify three-dimensional modeling as a pre-requisite for general solutions of combined loads. To our best knowledge, however, few studies have been conducted on torsional behavior of concrete beams which most of them are experimental investigations or simplified analytical models based on early and modified version of Compression Field Theory (M-CFT). Previous researchers focused on the torsional behavior of plain and reinforced concrete beams as well as FRP strengthened RC beams. However, the focus of this study is to find a rational set of constitutive laws of materials to simulate a three-dimensional reinforced concrete element. From the viewpoint of constitutive modeling of RC elements, there are two approaches; discrete crack and continuum level models. The major disadvantage that adheres to discrete crack models is the fact that these models focus on a local crack behavior and seeking to detect the crack paths, requiring a high computational cost. By contrast, continuum level models taking advantage of the spatially averaged macroscopic models to predict the structural behavior of the entire member (i.e. columns, beams etc.). In this method, the control volume of simulation is a finite domain between two primary transverse cracks which contains several secondary bond cracks, leading to relatively low computational cost along with acceptable accuracy. Furthermore, there are two major approaches for simulation of RC elements in continuum level; smeared cracks models and the models based on classical theory of plasticity. Smeared cracks models originally have been developed as a solution for 2D problems. Nevertheless, most of plasticity based models originally have been developed for 3D problems. The downside of plasticity based models however, is the uncertainty in calibration of material constant because most of these models are phenomenological models, not a physical consistent rule. Taking advantage of classical theory of plasticity along with damage mechanics, Lubliner et. al. (1989), proposed an isotropic Damage Plasticity Model for simulating the plain concrete. However, variety of researchs have been conducted on reinforced concrete members based on damage plasticity model. This model, includes material parameters such as dilation angle, yield surface factors etc,. which should be calibrated for each problem. The aim of this study is to investigate the effect of each parameter on the numerical response of the beam. Hence, solid RC beams under pure torsion have been simulated using nonlinear finite elements. Concrete material is simulated using isotropic plastic-damage model integrated in ABAQUS software. The constitutive laws of materials is modified using present methods to take into account for anisotropic behaviour of RC elements under torsion. The torque – twist curves, crack patterns and detected failure modes obtained from the proposed nonlinear finite element analysis are in good agreement with experimental results.