Modeling and numerical analysis of damage behavior of concrete

Any structure in the fields of engineering is prone to various kinds of loading conditions and unfavorable environmental impact during its lifespan. Consequently, damages are introduced to the structure. Further accumulation and propagation of the damage may eventually lead to complete failure. Thus, unpredictable failures of structures or structural components lead to serious economic consequences. Any structural failure is caused by the failure of materials used in construction. Therefore, the design rules of structures must incorporate the nonlinear deformation behavior of materials such as initiation of damage/crack and its propagation. In the presence of expensive experimental approaches, modeling approaches based on continuum damage mechanics have been serving as alternative and efficient computational tools to describe the failure mechanisms of diverse materials. Several damage models have been developed to simulate the monotonic deformation behavior of concrete. If complex loadings such as earthquakes or impacts are considered, cyclic and dynamic aspects of loading must be additionally taken into account. For this purpose, a 3D continuum damage model is formulated using a unified equivalent strain, which depends on invariants of elastically predicted stresses. The failure of concrete in tension and compression is characterized by softening behavior. Two history deformation variables are introduced to describe the unilateral behavior (i.e., crack opening and closure) effectively. The implicit-gradient method is also incorporated for regularizing the boundary value problem. The nonlocal equivalent strain and the history parameter are combined by a single damage loading function. To capture the irreversible permanent strains, a failure surface is included and also enabled for crack opening/closure. The proposed models with and without the incorporation of inelastic strains show qualitatively and quantitatively very good agreement with experimental results from the literature. Applications of the model are finally presented to demonstrate the ability and effectiveness of the model in predicting fracture phenomena such as crack initiation and propagation.