An Energy-based Damage Model for Concrete Structures under Cyclic Loading

An anisotropic damage model is developed by introducing nonlinear unloading/linear reloading branches on the principal axis of damage to simulate the hysteretic behaviors of concrete structures subjected to cyclic loading. The nonlinear unloading branch is defined as a power function and an energy-based evolution rule of damage is implemented into the definition of linear reloading one. Two independent damage variables, one for tension and the other for compression, are defined as a function of the ratio of accumulated dissipating energy to fracture energy to reflect the stiffness degradation caused by tensile cracking and compressive crushing. The calibrating procedures for key parameters are presented based on the stress-strain response obtained from the uniaxial cyclic tension or compression. A cyclic compressive test is analyzed with this model. The calculated responses are consistent with the experimental ones and reflect the stiffness degradation, the accumulation of irreversible deformation and hysteretic behaviors. The results show the anisotropic damage model is applicable to the nonlinear analysis of concrete structure under cyclic loading.