Concrete creep has become one of the major problems that threatens concrete structural development and construction. However, a reasonable and accurate calculation model for numerical analysis is the key to control and solve the creep deformation of concrete. To better describe the concrete nonlinear creep damage evolution rule, the visco-elasticity Plasticity Rheological Theory, Riemann Liouville Theory and Combined Model Theory are quoted, and the Able dashpot is used to reconstruct fractional-order soft-body composite elements to propose the expression of the stress-strain relationship of the elastomer, visco-elasticity plasticity body, and Viscoplasticity body, considering the evolution of the concrete compression damage process. A nonlinear creep damage constitutive model of concrete, based on fractional calculus theory, is conducted, and the parameters of the specific calculation method of the model are given. The influence of stress level σ, fractional order n and material parameter α on the concrete creep process is determined by a sensitivity analysis of the model parameters. The creep process and deformation amount of concrete in practical engineering can be effectively controlled by the results of the proposed sensitivity analysis. The research results can be used to provide guidance and reference for the safe construction of concrete engineering in actual practice.

The addition of alkali-resistant glass fiber to concrete effectively suppresses the damage evolution such as microcrack initiation, expansion, and nucleation and inhibits the development and penetration of microcracks, which is very important for the long-term stability and safety of concrete structures. We conducted indoor flat tensile tests to determine the occurrence and development of cracks in alkali-resistant glass fiber reinforced concrete (AR-GFRC). The composite material theory and Krajcinovic vector damage theory were used to correct the quantitative expressions of the fiber discontinuity and the elastic modulus of the concrete. The Weibull distribution function was used and an equation describing the damage evolution of the AR-GFRC was derived. The constitutive equation was validated using numerical parameter calculations based on the elastic modulus, the fiber content, and a performance test of polypropylene fiber. The results showed that the tensile strength and peak strength of the specimen were highest at a concrete fiber content of 1%. The changes in the macroscopic stress–strain curve of the AR-GFRC were determined and characterized by the model. The results of this study provide theoretical support and reference data to ensure safety and reliability for practical concrete engineering.