Abstract The non-ordinary state-based peridynamics (NSPD) is a promising method for fracture analysis, and it can incorporate the constitutive relationship of classical continuum mechanics in peridynamics. However, the high computational cost is one of the main reasons limiting its usage. To improve computational efficiency of NSPD, a stability-enhanced peridynamic (PD) element is proposed to couple NSPD with finite element method (FEM), primarily for fracture analysis. Only the areas where cracks may initiate or propagate are solved with the proposed PD element, while the rest of the model is composed of conventional finite elements. The main feature of the proposed PD element is attributed to that the bond interaction does not have to be parallel to the bond direction in NSPD, and the stability of the element is enhanced by introducing the improved hourglass method into the element to restrain the instability due to the zero-energy mode. Based on the equation of motion of NSPD and the principle of virtual work of the PD element, the stiffness matrix of the PD element is derived and the coupled NSPD and FEM method with a global stiffness matrix is thus established. Meanwhile, a two-step interface correction method is developed to improve the accuracy at the interface of the two domains. Subsequently, to verify the proposed coupling method, the uniaxial tension of a strip plate, the propagation of longitudinal wave, the compact tension test of a steel plate, and the single edge notched tension test of an orthotropic lamina are simulated. With the proposed coupling method, the fracture process is accurately simulated, while the computing time is significantly reduced by up to more than 80% when compared with the one using NSPD alone. Moreover, with the constitutive relationship represented by the elastic tensor, the orthotropic materials can be easily modeled in the proposed PD element, and the stress-based criteria can be used with minor modifications. The proposed coupled NSPD and FEM method has high accuracy, computational efficiency, and convenience, and it has the potential to be a useful tool for quantitative analysis of complex engineering fracture problems.

中文翻译：

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一种稳定性增强的近场动力学单元，用于将基于非普通状态的近场动力学与有限元方法耦合用于断裂分析

摘要 基于非常态状态的近场动力学（NSPD）是一种很有前景的断裂分析方法，它可以结合近场动力学中经典连续介质力学的本构关系。然而，高计算成本是限制其使用的主要原因之一。为了提高 NSPD 的计算效率，提出了一种稳定性增强的近场动力学 (PD) 单元，将 NSPD 与有限元法 (FEM) 结合起来，主要用于断裂分析。仅使用建议的 PD 单元求解裂纹可能开始或扩展的区域，而模型的其余部分由常规有限元组成。所提出的 PD 元件的主要特征归因于键相互作用不必平行于 NSPD 中的键方向，通过在元件中引入改进的沙漏法来抑制零能量模式引起的不稳定性，提高了元件的稳定性。基于NSPD的运动方程和PD单元的虚功原理，推导了PD单元的刚度矩阵，从而建立了具有全局刚度矩阵的NSPD与FEM耦合方法。同时，开发了一种两步界面校正方法，以提高两个域界面处的精度。随后，为了验证所提出的耦合方法，模拟了带状板的单轴拉伸、纵波的传播、钢板的紧凑拉伸试验和正交各向异性薄板的单边缺口拉伸试验。使用所提出的耦合方法，可以准确地模拟断裂过程，而与单独使用 NSPD 相比，计算时间显着减少了 80% 以上。此外，通过弹性张量表示的本构关系，可以在所提出的 PD 单元中轻松模拟正交各向异性材料，并且可以使用基于应力的标准，只需稍作修改。所提出的NSPD和FEM耦合方法具有高精度、计算效率和便利性，有可能成为复杂工程裂缝问题定量分析的有用工具。只需稍作修改即可使用基于压力的标准。所提出的NSPD和FEM耦合方法具有高精度、计算效率和便利性，有可能成为复杂工程裂缝问题定量分析的有用工具。只需稍作修改即可使用基于压力的标准。所提出的NSPD和FEM耦合方法具有高精度、计算效率和便利性，有可能成为复杂工程裂缝问题定量分析的有用工具。