A unified constitutive model for ultra-high performance concrete: Uniaxial evolution criteria, energy equivalent strain and multiaxial plastic damage model

In this study, a plastic damage constitutive model for ultra-high performance concrete (UHPC) is developed to facilitate the nonlinear analysis and performance assessment of UHPC structures. Based on the principles of irreversible thermodynamics and internal variable theory, the model systematically integrates plasticity and damage within a unified energy framework. The explicit form of the elastoplastic Helmholtz free energy potential is derived, and the damage energy release rate, defined as the thermodynamic conjugate to the damage variable, is introduced as the driving force for damage evolution. Uniaxial cyclic tests are employed to establish the evolution criteria of the internal variables under uniaxial stress states. Furthermore, the concept of energy equivalent strain is introduced to bridge the theoretical gap between uniaxial and multiaxial constitutive models, enabling the formulation of evolution criteria for internal variables under general multiaxial stress conditions. Finally, the applicability and accuracy of the proposed constitutive model are validated through a series of material tests and structural member experiments. The results demonstrate that the proposed model accurately captures the development of plastic deformation and the process of damage evolution in UHPC, providing a reliable theoretical foundation for the nonlinear analysis of UHPC structures.