A novel damage model in the peridynamics-based cohesive zone method (PD-CZM) for mixed mode fracture with its implicit implementation

Peridynamics (PD) becomes increasingly promising in computational fracture mechanics for its powerful ability to capture complex crack problems. Nevertheless, the PD applications are mainly limited to brittle fracture, and a robust PD model for predicting mixed mode fracture of quasi-brittle materials is still lacking. In this work, a novel damage model is proposed in the PD-CZM to accurately predict quasi-brittle failure under quasi-static mixed-mode loading, especially shear-dominated loading. In order to establish the damage criterion of quasi-brittle materials, the bond potential in bond based peridynamics (BBPD) is firstly separated into the dilatational part and deviatoric part. Instead of using existing bond stretch-based failure criterion, a new damage criterion obtained by combining bond stretch and dilatational bond potential is firstly proposed to determine the damage initiation. Also, the tension softening behavior of quasi-brittle materials is described in the damage model by a well-established degradation curve based on an energy-equivalence principle. Besides, to robustly solve the physical nonlinear characteristics, especially tension softening-induced snap-back phenomenon, the implicit implementation of the PD-CZM is performed with different implicit solution methods. Three challenging benchmarks are simulated to validate the proposed damage model, including Schlangen's single-edge notched beam test, Nooru-Mohamed's double edge-notched concrete specimen (DENS) test and Arrea and Ingraffea's single notched shear beam test with severe snap-back behavior. Both the predicted crack paths and the load–displacement curves are in perfect agreement with the experimental observations and other numerical results, clearly demonstrating the validity of the proposed damage model and the robustness of the implicit implementation.