Gradient-enhanced Coupled Plasticity-anisotropic Damage Model for Concrete Fracture: Computational Aspects and Applications

It is widely studied that classical continuum damage theory for concrete fracture exhibits an extreme sensitivity to the spatial discretization in the finite element simulations. This sensitivity is caused by the fact that the mathematical description becomes ill-posed at a certain level of accumulated damage. A well-posed problem can be recovered by using a gradient-enhanced damage model in which a material length scale is introduced as a localization limiter. In this work, a nonlocal gradient-enhanced fully coupled plastic-damage constitutive model for plain concrete is developed. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. In order to account for different effects under tensile and compressive loadings, nonlocal damage variables that account for the progressive degradation of mechanical properties under stress states of prevailing tension and compression and two internal length scales, one for tension and the other for compression, are introduced as localization limiters. Therefore, two nonlocal damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. In order to solve the time step problem, a decoupled elastic predictor and plastic corrector steps are performed first in the effective configuration where damage is absent, and then a nonlocal damage corrector step is applied in order to update the final stress state. The algorithmic treatment of both tension and compression is presented in a unified way. A simple procedure to calculate the gradient of the tensile/compressive damage variables is described which can be used directly without the need of intensive numerical modifications of an existing finite element code. The effectiveness of the proposed local model has been demonstrated in both uniaxial and biaxial tension and compression problems and compared with experimental data. Numerical results obtained with the proposed nonlocal model are compared with experimental results concerning bending of three-point notched and four-point notched concrete beams. As the mesh is refined, convergence of numerical results is observed both in terms of damage patterns and of the global response.