Abstract A generalized bond-based micropolar peridynamic model is proposed to simulate the nonlinear deformation and mixed-mode crack propagation of quasi-brittle materials under arbitrary dynamic loads. The mechanical behaviors of the material points are reformulated by incorporating the bond tension–rotation–shear coupling effects, which makes the model suitable for complex discontinuous problems in both three-dimensional spatial and two-dimensional plane conditions. The governing equations of the bond are established by employing the Timoshenko beam theory to simulate the interaction between material points as well as the bond coupling effect. Three kinds of peridynamic parameters, corresponding to the compressive, shear and bending stiffness of the bond, are introduced to keep the consistence of the strain energy obtained from the proposed peridynamic model and from the continuum mechanics under arbitrary deformation fields. Moreover, a novel energy-based failure criterion, involving the maximum stretch, shear strain and rotation angle limits of the bond, is proposed to describe the nonlinear behaviors and progressive failure for general quasi-brittle materials. The proposed model is verified by providing comparisons between its results and those from known analytical solutions and experimental observations. The influences of the bond tension–rotation–shear coupling effect as well as the applicability of the proposed model for the wave propagation, complex deformation and mix-mode fracture problems are also investigated. Results show that the proposed model with the bond coupling effect will greatly improve the simulation accuracy for dynamic problems of quasi-brittle materials under complex loading conditions. Results also indicate that the proposed model can well capture the nonlinear deformation, crack propagation, as well as progressive failure of materials with variable Poisson’s ratios under complex combined loads

中文翻译：

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具有键张力-旋转-剪切耦合效应的准脆性材料的基于键的广义近场动力学模型

摘要 提出了一种基于广义键的微极近场动力学模型来模拟任意动态载荷下准脆性材料的非线性变形和混合模式裂纹扩展。通过结合键张力-旋转-剪切耦合效应重新制定材料点的力学行为，这使得该模型适用于三维空间和二维平面条件下的复杂不连续问题。利用Timoshenko梁理论模拟材料点之间的相互作用以及键耦合效应，建立了键的控制方程。三种近场动力学参数，对应于粘结的压缩、剪切和弯曲刚度，被引入以保持从所提出的近场动力学模型和从任意变形场下的连续介质力学获得的应变能的一致性。此外，提出了一种新的基于能量的破坏准则，包括键的最大拉伸、剪切应变和旋转角限制，用于描述一般准脆性材料的非线性行为和渐进破坏。通过提供其结果与已知分析解决方案和实验观察结果之间的比较来验证所提出的模型。还研究了键张力-旋转-剪切耦合效应的影响以及所提出的模型对波传播、复杂变形和混合模式断裂问题的适用性。结果表明，所提出的具有键耦合效应的模型将大大提高复杂加载条件下准脆性材料动力学问题的仿真精度。结果还表明，所提出的模型可以很好地捕捉复杂复合载荷下具有可变泊松比的材料的非线性变形、裂纹扩展以及渐进破坏。