## 1 Introduction  
In recent years, fiber or mineral materials have been used to improve concrete performance given the disadvantages of ordinary concrete such as having great brittleness, having poor corrosion resistance and being easy to crack. Adding basalt fibers and polypropylene fibers in concrete cannot only enhance the strength of the concrete matrix but also improves the impact resistance performance and the durability of the concrete, and thus these have good application prospects [1; 2; 3; 4]. Except for their similar line expansion coefficients, the bond performance between steel bars and concrete is the essential reason that the two can work together. In concrete structures, due to the bond performance between concrete and steel bars, the external force loading on this element is resisted by the concrete and steel bars together. Bond performance directly affects stress transfer efficiency, and it also affects the bearing capacities and working performances of reinforced concrete structures and members. Accurate predictions for the nonlinear responses of steel bars and concrete can be made using the finite element method, which depends on the performance of the concrete under multiaxial stress conditions and the bond-sliding constitutive relationship between the steel bars and the concrete. The bond-sliding constitutive relationship is necessary to determine the stiffness matrix and the connecting unit in a finite element simulation. In recent years, many prediction models for determining the bonding constitutive relationship between steel bars and concrete have been proposed by scholars. The first cyclic load test on axial tensile steel bars in a specimen was conducted by [PERSON] et al. [5]. They studied the bond degradation mechanism under cyclic loads. Then, they reported the results of the bond's stress distribution and end slip measurements. [PERSON] et al. [6] recorded the end slip, embedded rod elongation and crack formation and extension in concentric tensile specimens. A bond stress-sliding prediction model related to the load size, thickness of the concrete cover and concrete strength was derived from the test data. [PERSON] et al. [7] discussed the bond-sliding mechanism in detail, and they proposed a parameter representing the concrete cover and constraint capacity of the stirrup and established a model of the deformation reinforcement bond sliding for crack-breaking and pull-out failures. The model could better predict the bond-slip behaviors of deformed bars with different constraint levels. Using a pull-out test, [PERSON] et al. [8] studied the effect of adding steel fiber on a steel bond's performance, and they proposed a new steel bond model. For a more realistic bond-slip analysis, the finite initial bond stiffness was considered in addition to the influence of the steel fiber. [PERSON] et al. [9] evaluated the effects of the concrete cover and the fiber volume fraction on the bond properties of concrete using beam specimens. Based on their experimental results and early research, a bond stress-sliding response model for steel bars embedded in ordinary concrete and in steel-fiber concrete was proposed, and the constitutive relationship describing its characteristic behaviors was established. The tensile strengths, splitting strengths and bending strengths of concrete mixed with polypropylene and basalt fibers have been effectively improved, and the ductility, toughness and impact resistance of concrete have been significantly improved. Therefore, hybrid fiber-reinforced concrete is very different from ordinary concrete. There are obvious differences between the basic theory for hybrid fiber-reinforced concrete and steel bars and the existing theory for ordinary reinforced concrete. The early proposed bond-slip constitutive relationship between steel bars and concrete does not describe all the elements of the bond performance, especially that between steel bars and fiber-reinforced concrete.