A Practicable Elastoplastic Damage Model for Concrete with Decoupled Plasticity and Damage

In this paper, a practicable elastoplastic damage model with decoupled plasticity and damage for concrete is proposed. Plastic strain is evaluated in the effective stress space through an empirical relation, allowing the plastic and damage processes to be treated separately and simplifying the constitutive calculation. Within an irreversible thermodynamics framework, the damage criterion is formulated in terms of the damage energy release rate derived from a modified elastic Helmholtz free energy expression. The free energy function is separated into hydrostatic and deviatoric parts. The direct hydrostatic contribution to the damage-driving force is omitted, while a stress-state-dependent coefficient modifies the deviatoric contribution under multiaxial stress states. Spectral decomposition of the effective stress tensor provides positive and negative parts, enabling separate evolution of tensile and compressive damage. Independent tensile and compressive damage variables are combined through a weighted scalar damage measure to represent their interaction and the tension-compression softening effect. The proposed model retains a simple mathematical structure while incorporating plastic deformation, stiffness degradation, damage evolution, and loading-state dependence within a unified framework. Comparison with experimental data shows that the relative error and peak stress error for the biaxial strength envelope are 1.5% and 0.9%, respectively, while the peak stress errors for uniaxial and biaxial compression are 0.71% and 0.55%, respectively. The first three natural circular frequencies of the Koyna concrete dam predicted by the model are 18.86, 49.98, and 68.16 rad/s, showing close agreement with published reference results. These results demonstrate the applicability of the proposed formulation to nonlinear numerical analysis of concrete materials and structures.