Formulation and efficient implementation of coupled anisotropic damage-plasticity model for plain concrete

The formulation and finite element implementation of an efficient anisotropic damage-plasticity model is proposed to simulate the nonlinear behavior of plain concrete at small strains. The model's formulation is presented first; then, the implementation strategy is described. A stress-based yield criterion and two damage criteria are used to determine the nominal stress tensor. Using two damage tensors automatically accounts for the stiffness recovery in transition from tension to compression and vice versa. Some numerical issues are addressed, and the remedy is proposed. The deficiencies of existing anisotropic damage-plasticity models for plain concrete are also identified and discussed. Different alternatives for the general formulation of damage procedure are presented and compared. Three methods are introduced for calculation of damage hardening parameters and compared in terms of efficiency. The extension of the model to viscoplastic behavior is carried out using the frequently-used Duvaut-Lions viscoplasticity theory. Moreover, the formulation is extended to include the large crack in monotonic and cyclic loading, which improves the response of material under large values of strain. The model is included in an in-house finite element software previously developed by the authors. It is validated, and its efficiency is evaluated by comparing the software results with a set of experimental tests, such as monotonic uniaxial and biaxial tests, cyclic uniaxial tests, and some structural single-mode and mixed-mode tests.