Keywords: nonlinear analysis, constitutive modeling, reinforced concrete, Drucker-Prager criterion, von Mises criterion, finite element.

There is not a certain material model to predict the true behavior of reinforced concrete (RC) structures or to determine the ultimate capacity of RC structures. For this reason, concrete material constitutive modeling is still an active research subject. Until now, researchers developed many different material models by experimental or analytical studies, to describe the behavior of RC structures. In general, the behavior of RC structures is presented by stress-strain relationship which is represented by a stress-strain curve.

For RC, linear-elastic theory is generally used as a material model. But, in order to predict the true behavior of RC up to failure point, it is necessary to use elasto-plastic constitutive material model in the calculation of element stiffness matrix. In order to calculate the elasto-plastic constitutive material matrix, a variety of failure criteria have been proposed for concrete and metal materials. They can be classified as one-parameter, two-parameter, three-parameter, four-parameter and five-parameter models. For example, von Mises and Tresca can be classified as one-parameter model and Drucker-Prager can be classified as a two-parameter model. These parameters are the material constants. In Drucker-Prager criterion, they are cohesion and friction angle. Both Drucker-Prager and von Mises criteria are generally suggested for modeling concrete and metal materials.

The aim of this paper is to study materially nonlinear analysis of RC beams in a plane stress state. The study is carried out for three different cases. In the first case, the Drucker-Prager criterion is used to model both concrete and reinforcement. In the second case, von Mises is used to model both concrete and reinforcement. In the third case, Drucker-Prager is used to model concrete, and von Mises is used to model reinforcement. A computer program is devleoped, which includes the failure criteria mentioned above for both concrete and reinforcement. For concrete and reinforcement, four-node quadrilateral finite elements are used. The bond between concrete and reinforcement is assumed to be perfect. Using this assumption, the element stiffness matrix is constructed by assembling concrete and reinforcement elements stiffness matrices. The constitutive material matrix is presented in detail. The finite element method is used for spatial integration, and the incremental Newton-Raphson technique is used in the nonlinear solution process. It is concluded that the program developed in this study is capable of predicting the nonlinear behavior of reinforced concrete beams.

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