A Study On The Damage Constitutive Model For Concrete And Its Numerical Implementation

A large number of microstructural defects including microcracks and microvoids are scattered in concrete. The microcracks are expanded and the microvoids are crushed under complex loading conditions, which cause the nonlinear behavior of concrete, such as asymmetry in tension and compression, stiffness degradation, irreversible deformations, unilateral and rate effect, anisotropy, and localization of deformation and damage, etc. In damage theory, the microdefects are averaged within the range of characteristic size. And to consider the distribution and development of microdefects at the macro level, a damage variable is introduced into constitutive model to quantitatively evaluate the grade of deterioration of concrete structures. Hence, both the macroscopic mechanical behavior and microstructural changes and interactions can be considered, simultaneously. Therefore, a bridge is built between the macroscopic level and the microscopic material structure.The research situations of concrete damage theory at home and abroad are summarized and several issues, such as damage surface and energy release rate are discussed in detail. Based on the thermodynamic theory and experimental phenomena, the damage constitutive models are improved and applied in engineering.(1) An elastic-damage model is improved. In order to consider the microcrack closure effect, the Helmholtz free energy is decomposed into hydrostatic and deviatoric components, and a unilateral effect function is introduced into the hydrostatic part. Based on elastic damage energy release rate, damage surface is built. According to the thermodynamics theorem, damage evolution rule is obtained. In the improved model, fewer parameters and simpler formulation are used and numerical calculation is more convenient than traditional one. The model is employed in the analysis of a gravity dam subjected to earthquake loading. Numerical results show that the proposed model has good convergence and high computation efficiency in the nonlinear analysis of large-scale engineering structures.(2) An anisotropic damage model is improved. The second-order damage tensor is used to characterize the anisotropy induced by the orientation of microcracks. In order to keep the symmetry of nominal stress, the hydrostatic and deviatoric damage effect tensors are proposed. Damage criterion is constructed by equivalent energy release rate and equivalent damage variable. According to the thermodynamics theorem, damage evolution rule is obtained. Parameters in the model are easily obtained from experiment tests and the state variable is directly updated by employing explicit algorithm. Numerical results of concrete tests under uxiaxial compression show that the proposed model is capable to simulate the distribution and direction for microdefects.(3) An epalstoplastic damage model is improved. The plasticity behavior is represented in effective stress space by a single plastic yield surface, in which the effect of hardening conditions and Lode angle is considered. Especially, the plastic yield surface is smooth without comers for plane problem, and with a corner for three-dimensional problem. The plastic Helmholtz free energy is improved in a detail. Results of numerical examples by the improved model agree well with the test results of specimens under uniaxial tension and compression, biaxial loading and triaxial loading. Failure processes of single-edge-notched (SEN) beam and double-edge-notched (DEN) specimen are also simulated to further validate the proposed model.(4) Based on the rate-independent model, a rate-dependent model is developed by introducing Duvaut-lions viscosity concept into the inelastic strain and damage variable, respectively. Rate sensitivity of concrete in the elastic phase is taken consideration in the proposed constitutive model via an elastic additional condition. Numerical simulation of experiments with rate effect validates capacity of the model for the rate dependent of concrete.(5) The displacement is selected as nonlocal variable, then a nonlocal damage model is developed incorporated with a modified plastic damage model, and is used in the structure analysis. The nonlocal energy release rate is calculated by nonlocal displacement, and consequently the evolution of nonlocal damage is simulated. An improved gradient coefficient including boundary and damage effects is introduced to eliminate pseudo-damage on the boundary. A benchmark and a three-point bending beam test with different finite element meshes are analyzed. The numerical results show that it is capability to capture the post-peak softening behaviour and reach mesh-independent results.(6) Numerical algorithms and computational procedures are given at the local and global level for each constitutive model. For the local level, fully implicit backward-Euler difference scheme is employed to discretize constitutive equations. For elastic damage and anisotropic damage model, all the internal variables can be updated immediately except the energy release rate and damage multiplier, which are updated by Newton iteration. A multiplier split algorithm for plastic damage model is implemented though three steps, i.e., elastic prediction, plastic correction, and damage correction. In the step of plastic correction of three dimension problems, the return mapping algorithm for smooth portion and apex portion are considered separately. Guaranteeing convergence, the formulation of algorithmic consistent tangent module is particularly given rather than continuum consistent tangent module. For the global level, the problem of negativity stiffness caused by softening behavior is solved by the arc-length method. Based on the element stiffness of local damage model, the nonlocal element stiffness is obtained by nonlocal correction, and it can be directly implanted to the traditional FEM by broadening the bandwidth of the local element stiffness matrix.