Research On Fracture And Damage Of Concrete Based On The Enhanced Damage Model

The failure of concrete is very complicated as the micro-cracks of concrete existence and non-uniformity of the material itself. Damage mechanics by introducing a set of field variables can describe not only the existence and the growth of the micro-cracks or micro-defects of concrete but also the failure and fracture of concrete. The very fact that damage mechanics use a continuous representation of crack renders them particularly suitable for numerical simulations. However the localization of damage is in contradiction with the supposed smoothness of the damage field and thus the finite element solution based on damage model depend heavily on the spatial dispersion. As denser mesh, the growth of damage tends to localize in the smaller possible volume. Nonlocal damage mode and the gradient-enhanced damage model by introducing the space interaction into the constitutive relations can overcome the pathological mesh dependence when damage of concrete is simulated.The domestic and foreign research of fracture and damage of concrete are reviewed according to extensive literature and then the solutions to the mesh dependence in the finite element numerical analysis for fracture and damage of concrete are summarized in this paper.One of the focuses of this paper is to research nonlocal damage model. Based on the non-uniform of micro structural of concrete, the smooth weight function is introduced to substitute for the piecewise uniform weighting which has been implicitly assumed in the classical non-local model and therefore a new non-local damage model is built. B-Spline and Gauss functions are used as weight functions to find solutions to nonlocal equivalent strain in the nonlocal damage model. A board with mode -I crack is used a calculation model for numerical calculation. Furthermore, nonlocal damage model and finite element numerical analysis are used for concrete strain softening and damage localization. Its result is compared with the result of numerical results of local damage model. The analytical results prove that nonlocal damage model with smooth weight function can effectively eliminate the pathological mesh dependence in the finite element numerical analysis.Another focus of this paper is to research gradient damage model. Firstly, the faults of implementation of finite element of non local damage model are analyzed, and by expanding nonlocal equivalent strain into Taylor series, explicit gradient model and implicit gradient model is constructed. Control equations of implicit gradient model remain elliptic during the whole damage process, which is proved by derivation of control equations of the implicit gradient model. The relationship of implicit gradient model and nonlocal model is discussed. Secondly, Boundary conditions of implicit gradient models are analyzed. The numerical extrapolated method for calculation of nonlocal equivalent strain at the crack tip of concrete board under uniformly distributed loads is presented while the strain field was discussed and the supposed smoothness of the damage field is ensured in the complicated internal boundary. In the complicated space stress, effective damage matrix is introduced and anisotropic nonlocal damage model based on the implicit gradient formula is constructed. Finally, finite element implementation of the implicit gradient model is discussed and the defining principle of the interpolations functions is studied during the finite element implementation. The model is applied to numerical simulation of damage of a concrete board with mode -I crack and a three-point bending concrete beam.In the end, research is performed on the implicit gradient model in the high-cycle fatigue damage and a new method—fatigue damage algorithm based on nonlocal strengthened gradient damage model is presented for calculating the fatigue life. The numerical calculation result of bar with a single lateral is compared with the result of Paris formula.