A plastic damage model for concrete structure cracks with two damage variables

Based on the concepts of continuum damage theory, a new plastic damage model for concrete crack failure is developed through studying the basic damage mechanics. Two damage variables, tensile damage variable for tensile damage and shear damage variable for compressive damage, are adopted to represent the influence of microscopic damage on material macro-mechanics properties under tensile and compressive loadings. The yield criteria and flow rule determining the plasticity of concrete are established in the effective stress space, which is convenient to decouple the damage process from the plastic process and calibrate material parameters with experimental results. Meanwhile, the plastic part of the proposed model can be implemented by back-Euler implicit algorithm, and the damage part is explicit. Consequently, there exist robust algorithms for integrating the constitutive relations using finite element method. Comparison with several experimental results shows that the model is capable of simulating the nonlinear performance of concrete under multiaxial stress state and can be applied to practical concrete structures.