Strain based approach in fatigue damage modeling of brittle material-application to concrete

Due to very good compressive strength of concrete, it is used widely in all over the world during three decades. The Formulation of Concrete is through combination of Cement, stone aggregate, sand and water according to their design mix based on the ultimate strength required for the structural component. The Mixing of concrete is as mortar, the layer of cement, sand and water is wrapped around the aggregate. When the load is applied to the concrete, the weaker zone i.e. mortar of cement, sand is weaker than stone aggregate, damage by formulation of crack before crack in aggregate. The Damage behavior of Concrete is thus to be analyzed according to their fatigue behavior. Strain Based approach in Fatigue Damage Modelling of Brittle Material in Concrete is presented to describe the behavior and failure of con-crete by utilizing Damage Mechanics approach. Stiffness degradation and inelastic deformation are the essential features of concrete that develop due tothe formation of multitude of microcracks in the fatigue environment. Microcracking, which is anisotropic in nature, destroys the bond between material grains, and affects the elastic properties resulting in the reduction of material stiffness in elastic as well as plastic stage. This paper presents an anisotropic fatigue damage model for plain concrete subjected to cyclic tension. The model is developed, in strain space, using the general framework of internal variable theory of continuum thermodynamics and Damage Mechanics. It is argued that within the damage surface of given strain states the unloadingreloading cycles (fatigue loading) stimulate the nucleation and growth microcracks in concrete, which will result in stiffness degradation and inelastic deformation, and hence material is termed as damaged. Damage is reflected through the fourthorder stiffness tensor involving a damage parameter whose increment is governed by the consistency equation associated with a cycle dependent damage surface in strain space. The model is capable of predicting stiffness degradation, inelastic deformation and strength reduction under fatigue loading and compared against experimental result. By increasing the number of loading cycles, the strength of concrete gradually decreases and the limit surface is allowed to contract and form new curves representing residual strengths. The magnitude of loading, load range, and the load path are known to influence the fatigue life and hence are addressed in this formulation. In this paper, a strength softening function is proposed in order to address the re-duction in the strength of concrete due to fatigue. Separate softening functions are also proposed to account for the deformation characteristics in concrete under cyclic loading. Numerical simula-tions predicted by the model in both uniaxial and biaxial stress paths show a good correlation with the experimental data available in the literature.