Finite Element Analysis of Concrete Structures Using Plastic Damage Model in 3 D Implementation

Neither damage mechanics model nor elastoplastic constitutive law can solely describe the behavior of concrete satisfactorily. In fact, they both fail to represent proper unloading slopes during cyclic loading. To overcome the disadvantages of pure plastic models and pure damage approaches, the combined effects need to be considered. In this regard, various classes of plastic damage models have been recently proposed. Here, the theoretical basics of the plastic damage model originally proposed by Lubliner et al. and later on modified by Lee and Fenves is initially presented and its numerical aspects in three dimensional space are subsequently emphasized. It should be mentioned that a part of the implementation in 3 D space needs to be reformulated due to employing a hyperbolic potential function to treat the singularity of the original linear form of plastic flow proposed by Lee and Fenves. The consistent algorithmic tangent stiffness, which is utilized to accelerate the convergence rate in solving the nonlinear global equations, is also derived. The validation and evaluation of the model to capture the desired behavior under monotonic and cyclic loadings are shown with several simple one element tests. These basic simulations confirm the robustness, accuracy, and efficiency of the algorithm at the local and global levels. At the end, a four point bending test is examined to demonstrate the capabilities of the model in real 3 D applications.