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.

Peridynamics（PD）因其强大的捕获复杂裂纹问题的能力而在计算断裂力学中变得越来越有希望。然而，局部放电的应用主要限于脆性断裂，并且仍然缺乏用于预测准脆性材料的混合模式断裂的鲁棒的局部放电模型。在这项工作中，PD-CZM中提出了一种新颖的损伤模型，以准确地预测准静态混合模式载荷（尤其是剪切为主的载荷）下的准脆性破坏。为了建立准脆性材料的破坏准则，在基于键peridynamics粘结电位（BBPD）首先分离为疏密部分和偏部分。代替使用现有的基于键拉伸的破坏准则，首先提出了通过结合键拉伸和膨胀键势获得的新的破坏准则来确定破坏的开始。同样，在损伤模型中，通过基于能量等效原理的成熟的降解曲线来描述准脆性材料的拉伸软化行为。此外，为了稳固地解决物理非线性特性，特别是张力软化引起的回跳现象，PD-CZM的隐式实现是使用不同的隐式求解方法来执行的。模拟了三个具有挑战性的基准，以验证建议的损伤模型，包括Schlangen的单边缺口梁测试，Nooru-Mohamed的双边缺口梁混凝土试件（DENS）以及Arrea和Ingraffea的单缺口剪力梁试验，具有严重的回弹行为。预测的裂纹路径和载荷-位移曲线均与实验观察结果和其他数值结果完全吻合，从而清楚地证明了所提出的损伤模型的有效性和隐式实施的鲁棒性。