A novel non-linear peridynamic model for quasi-brittle materials under cyclic loading

•Simulation of quasi-brittle materials fatigue behaviour.•A novel non-linear PD law is proposed.•A calibration function and parameter are included in the law.•A parametric study is performed.•Validation of the proposed model is carried-out. In the present paper, a novel non-linear peridynamic (PD) model is proposed to numerically simulate the fatigue behaviour of quasi-brittle materials. The model implements a non-linear degradation law for the bonds, function of the number of loading cycles. More precisely, a calibration function and a calibration parameter are included in such a law. The novel PD model is applied to simulate cyclic three-point bending experimental tests performed on concrete notched beams (available in the literature). The results are presented in terms of fatigue lifetime, Paris law parameters and crack path.