Numerical Analysis of Cyclically Loaded Concrete Under Large Tensile Strains by the Plastic-Damage Model

Within the framework of plasticity-based constitutive laws, a plastic-damage model is developed in a complete form for analysis of damaged structures under large tensile strains which is suitable for concrete subjected to cyclic loadings. This is based on the plastic-damage model proposed by Lee and Fenves, which utilizes two separate damage variables for tension and compression and also a scalar degradation simulating damage on stiffness. Implementation of the model is coded for three-dimensional space in a special purpose finite element program to analyze the behavior of concrete subjected to large tensile cracking, which is inevitable in plain concrete structures. In order to include large crack opening/closing displacements in the model, the excessive increase in plastic strain causing unrealistic results in cyclic behaviors is prevented when the tensile plastic-damage variable controlling the evolution of tensile damage is larger than a critical value. To expedite the convergence rate for the overall equilibrium iterations, the consistent algorithmic tangent stiffness tensor is also derived, in detail, for large cracking states. The paper is completed with some numerical examples demonstrating the capability of the extended model in reproducing the behavior of cyclically loaded plain concrete subjected to large tensile strains.