Formulation and verification of an anisotropic damage plasticity constitutive model for plain concrete

This paper presents a new constitutive model based on the combination of plasticity and anisotropic damage mechanics to predict the nonlinear response of plain concrete. The aim is to overcome the deficiencies of the previous anisotropic damage-plasticity models in simulating concrete failure under multiaxial loadings. To effectively combine plasticity and damage, a decoupled algorithm and consequently a strain equivalence hypothesis are employed. A stress-based yield criterion and a non-associative flow rule are used in the plasticity formulation. The stress tensor is decomposed into positive and negative parts to consider the unilateral effect of concrete damage. Consequently, two sets of damage criteria and two anisotropic damage tensors are defined, which leads to automatically accounting for the stiffness recovery in transition from tensile to compressive stress. The viscous model of Duvaut–Lions is employed to improve mesh dependency. Moreover, the formulation is regularized to capture large crack opening and closing when the material has experienced large amounts of strain. The numerical implementation of the proposed model is described in detail. A special in-house finite element program incorporating the proposed approach is developed. The efficiency of the model is verified by comparing numerical results and experimental data for different benchmark problems such as monotonic and cyclic uniaxial tests, monotonic biaxial test, and mixed-mode multidimensional structural tests.