Energy-Consistent Mapping for Concrete Tensile Softening Within a Framework Combining Concrete Damaged Plasticity and Crack Band Theory

As concrete exhibits localized strain softening, for example, under tension, fracture-energy consistency is essential for obtaining mesh-insensitive results of finite-element (FE) analyses. Accordingly, element- and structural-level parametric studies of uniaxial tensile behavior are performed within an FE framework coupling the Concrete Damaged Plasticity (CDP) model, the Crack Band Theory, and the Newton–Raphson solver in Abaqus. The effects of several CDP parameters and the mesh size are quantified using a sensitivity index (SI). A damage evolution law with several tensile parameters is proposed for energy consistency in addition to scaling of the softening strain. Besides tensile strength, elastic modulus, and an estimated uniaxial stress–strain curve, three key parameters are validated: the ratio between fracture energy from pure tension in the crack band and that from direct-tension tests, and two mesh-independent damage evolution parameters. An inverse calibration is proposed, in which the damage parameters and the fracture-energy ratio are identified in one-element (SI≤5%) and multi-element models, respectively. With these calibrations, the tensile response of the crack band is obtained, and multi-element analyses achieve mesh insensitivity when meshes are not smaller than the crack-band width. For finer meshes violating continuum assumptions, the initial damage rate parameter is reduced to preserve energy consistency.