An improved unibond dual-parameter peridynamic model for fracture analysis of quasi-brittle materials

Peridynamics (PD) is a new nonlocal form of classical continuum mechanics, which is very suitable for investigating material failure. However, the application of classical bond-based PD (BPD) to brittle fracture is restricted because the failure models proposed in BPD mainly describe brittle fracture rather than quasi-brittle fracture. Moreover, the models have a limitation of fixed Poisson's ratio, and the effect of internal length on non local long-range forces cannot be reflected. The present study proposes an improved unibond dual-parameter PD (UDPD) model to overcome the three drawbacks in the damage and fracture analyses of quasi-brittle materials. The conversion formulations of the normal stiffness and tangential stiffness between the elasticity modulus and Poisson's ratio were derived first. Then, a continuous function was introduced in the UDPD model by considering the internal length effect of long-range forces, and the corresponding expressions of the micromodulus functions were deduced. Furthermore, the basic form of the constitutive force function of the UDPD was constructed based on the linear and nonlinear mechanical behaviors of the failure process of quasi-brittle materials, and a corresponding failure criterion was used to evaluate the damage. The validity and accuracy of the proposed model were demonstrated by conducting numerical tests on four specimens, namely, a rectangular plate, double-edge notched concrete specimen, unilaterally notched gray cast iron, and concrete L-specimen panel under quasi-static loading. The model results were compared with those of experiments and numerical studies in the literature. It was found that the proposed model has the same simplicity and stability of the BPD model and can fully capture the nonlinear deformation and progressive failure of quasi-brittle materials with different Poisson's ratios.