Abstract:To quantitatively characterize the fracture damage evolution mechanism inside concrete under cyclic loading, this paper systematically investigates the evolution laws of crack length, displacement gradient, and residual strain in the fracture process zone (FPZ) of concrete through three-point bending beam tests. A Tikhonov regularization-based cohesive stress inversion method is employed to invert the cohesive stress distribution, and the cohesive stress softening curve is obtained. The results indicate that under constant-amplitude loading, the crack length exhibits a two-stage characteristic of a rapid increase followed by nearly linear slow growth. The FPZ displacement gradient undergoes a two-stage attenuation process consisting of a steep decline followed by a gradual decline, with the attenuation magnitude at low load levels significantly higher than that at high load levels. Under envelope loading, the crack length continues to increase with the number of loading cycles and then tends to stabilize, whereas the FPZ displacement gradient decreases monotonically. The crack propagation rate lags behind the increase in crack mouth opening displacement, resulting in an increase in the width of the fracture process zone and a decrease in its length. Owing to the synergistic development of cohesive stress degradation, material damage, and plastic deformation induced by cyclic loading, the residual strain in the FPZ accumulates continuously over loading cycles at an accelerating rate. Based on the assumption of a linear distribution of FPZ opening displacement, the Tikhonov regularization method was used to invert the cohesive stress distribution. The resulting softening curve approximately follows a power-law form, and the inverted displacement field agrees well with the experimental data, thereby verifying the reliability of the inversion method.