Three-dimensional finite element analysis of reinforced concrete structural elements regarded as elastoplastic multiphase media

Abstract

Conceived as a generalization of the homogenization method, a multiphase modeling is developed to assess the macroscopic behavior of reinforced concrete slabs and beams within the framework of classical plasticity with account for concrete cracking. At the scale of structure, particular emphasis is given to the effects of the multiphase zone thickness adopted for numerical simulation. Similarly to the description at the macroscopic level of ordinary porous media, the macroscopic particle is regarded in the multiphase model as the geometrical superposition of continuous media in mutual interaction. The coincident (matrix particle and reinforcement particle) are given distinct kinematics. The equations of motion are derived by means of the virtual work method. The state equations for each phase and the interaction law are formulated within the framework of generalized plasticity. Using a three-dimensional finite element implementation, the multiphase approach is applied to analyze reinforced concrete beams and slabs under prescribed loading. The accuracy of the approach is assessed by means of experimental test data. In addition, the role of multiphase zone extent is investigated. The analysis showed a rapid convergence of the numerical prediction toward the experimental data when the multiphase zone thickness decreases, thus emphasizing the multiphase size independency of the model.