*Article* **Stress–Strain Behavior of FRC in Uniaxial Tension Based on Mesoscopic Damage Model**

**Weifeng Bai, Xiaofeng Lu, Junfeng Guan \* , Shuang Huang \*, Chenyang Yuan and Cundong Xu**

School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450046, China; baiweifeng@ncwu.edu.cn (W.B.); z20201010121@stu.ncwu.edu.cn (X.L.); yuanchenyang@ncwu.edu.cn (C.Y.); xucundong@ncwu.edu.cn (C.X.) **\*** Correspondence: junfengguan@ncwu.edu.cn (J.G.); z201710103065@stu.ncwu.edu.cn (S.H.)

**Abstract:** Fiber-reinforced concrete (FRC) is widely used in the field of civil engineering. However, the research on the damage mechanism of FRC under uniaxial tension is still insufficient, and most of the constitutive relations are macroscopic phenomenological. The aim is to provide a new method for the investigation of mesoscopic damage mechanism of FRC under uniaxial tension. Based on statistical damage theory, the damage constitutive model for FRC under uniaxial tension is established. Two kinds of mesoscopic damage mechanisms, fracture and yield, are considered, which ultimately determines the macroscopic nonlinear stress–strain behavior of concrete. The yield damage mode reflects the potential bearing capacity of materials and plays a key role in the whole process. Evolutionary factor is introduced to reflect the degree of optimization and adjustment of the stressed skeleton in microstructure. The whole deformation-to-failure is divided into uniform damage phase and local failure phase. It is assumed that the two kinds of damage evolution follow the independent triangular probability distributions, which could be represented by four characteristic parameters. The validity of the proposed model is verified by two sets of test data of steel fiber-reinforced concrete. Through the analysis of the variation law of the above parameters, the influence of fiber content on the initiation and propagation of micro-cracks and the damage evolution of concrete could be evaluated. The relations among physical mechanism, mesoscopic damage mechanism, and macroscopic nonlinear mechanical behavior of FRC are discussed.

**Keywords:** fiber-reinforced concrete; damage mechanism; uniaxial tension
